×

zbMATH — the first resource for mathematics

Applications of the theory of modular forms to number theory. (English) Zbl 0446.10021

MSC:
11F03 Modular and automorphic functions
11-02 Research exposition (monographs, survey articles) pertaining to number theory
11F11 Holomorphic modular forms of integral weight
11F12 Automorphic forms, one variable
11F33 Congruences for modular and \(p\)-adic modular forms
11F67 Special values of automorphic \(L\)-series, periods of automorphic forms, cohomology, modular symbols
11E45 Analytic theory (Epstein zeta functions; relations with automorphic forms and functions)
11N37 Asymptotic results on arithmetic functions
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] I. Abdullaev, ?Elliptic curves and the representation of numbers by quaternary quadratic forms,? Dokl. Akad. Nauk Uzb. SSR, No. 1, 3?4 (1973).
[2] I. Abdullaev, ?Formulas of Weil-Eichler type for the number of representations of any natural numbers by quadratic forms with four and six variables,? Izv. Akad. Nauk Uzb.SSR, Ser. Fiz.-Mat. Nauk, No. 3, 3?10 (1976).
[3] I. Abdullaev and L. A. Kogan, ?Elliptic curves and the representation of numbers by positive quadratic forms,? Dokl. Akad. Nauk Uzb. SSR, No. 6, 3?4 (1971).
[4] I. Abdullaev and L. A. Kogan, ?Elliptic curves and the representation of numbers by positive definite quadratic forms with four and six variables,? Vestn. Karakalp. Fil. Akad. Nauk Uzb. SSR, No. 4 (54), 15?18 (1973).
[5] I. Abdullaev and L. A. Kogan, ?Elliptic curves and the representation of numbers by positive quadratic forms with six variables,? Tr. Tashk. Politekh. Inst., No. 130, 17?22 (1974).
[6] V. A. Abrashkin, ?Finding two-class imaginary quadratic fields with even discriminant by the method of Heegner,? Mat. Zametki,15, No. 2, 241?246 (1974).
[7] A. N. Andrianov, ?Generalization of a theorem of M. Eichler from the theory of quaternary quadratic forms,? Dokl. Akad. Nauk SSSR,141, No. 1, 9?12 (1961). · Zbl 0107.26803
[8] A. N. Andrianov, ?On the analytic arithmetic of quadratic forms with an odd number of variables in connection with the theory of modular forms,? Dokl. Akad. Nauk SSSR,145, No. 2, 241?244 (1962). · Zbl 0133.29801
[9] A. N. Andrianov, ?Representation of numbers by certain quadratic forms in connection with the theory of elliptic curves,? Izv. Akad. Nauk SSSR, Ser. Mat.,29, No. 1, 227?238 (1965). · Zbl 0166.05403
[10] A. N. Andrianov, ?On representations of the modular group on space of parabolic forms,? Dokl. Akad. Nauk SSSR,165, No. 4, 735?737 (1965).
[11] A. N. Andrianov, ?Dirichlet series with Euler product in the theory of Siegel’s modular forms of genus 2,? Tr. Mat. Inst. Akad. Nauk SSSR,112, Part 1, 73?94 (1971). · Zbl 0224.10027
[12] A. N. Andrianov and O. M. Fomenko, ?On quadratic means in progressions of Fourier coefficients of parabolic forms,? Tr. Mat. Inst. Akad. Nauk SSSR,80, 5?15 (1965). · Zbl 0174.08302
[13] A. N. Andrianov and. O. M. Fomenko, ?The distribution of norms of hyperbolic elements and the number of classes of indeterminate binary quadratic forms,? Dokl. Akad. Nauk SSSR,196, No. 4, 743?745 (1971). · Zbl 0222.10025
[14] R. I. Beridze, ?On the representation of numbers by certain quadratic forms with four variables,? Tr. Tbilis. Univ.,102, 221?233 (1964).
[15] R. I. Beridze, ?On the representation of numbers by certain quadratic forms with eight variables. I, II,? Tr. Tbilis. Univ.,110, 303?322 (1965);117, 77?101 (1966).
[16] R. I. Beridze, ?On the representation of numbers by certain quadratic forms with four variables,? Soobshch. Akad. Nauk Gruz.SSR,50, No. 2, 267?273 (1968). · Zbl 0226.10025
[17] R. I. Beridze, ?On the representation of numbers by certain quadratic forms with eight variables,? Tr. Tbilis. Univ.,A1 (137), 5?16 (1971).
[18] A. A. Val’fish, ?On the representation of numbers by sums of generalized pentagonal numbers,? Soobshch. Akad. Nauk Gruz. SSR,22, No. 4, 385?392 (1959).
[19] A. Z. Val’fish, ?Additive number theory. XI,? Tr. Tbilis. Mat. Inst. Akad. Nauk Gruz. SSR,19, 33?59 (1953).
[20] A. Z. Val’fish, ?On sums of coefficients of some modular forms,? Soobshch. Akad. Nauk Gruz. SSR,16, No. 6, 417?423 (1955).
[21] A. Z. Val’fish, ?On sums of moduli of the coefficients of some modular forms,? Soobshch. Akad. Nauk Gruz. SSR,16, No. 7, 497?502 (1955).
[22] L. N. Vasershtein, ?On the group SL2 over Dedekind rings of arithmetic type,? Mat. Sb.,89, No. 2, 312?322 (1972).
[23] A. B. Venkov, ?On a series over a discrete group and its application to Dirichlet series connected with automorphic forms,? Zap. Nauch. Sem. Leningr. Otd. Mat. Inst. Akad. Nauk SSSR,63, 3?7 (1976).
[24] T. V. Vepkhvadze, ?On some formulas of Liouville,? Soobshch. Akad. Nauk Gruz. SSR,40, No. 2, 279?286 (1965).
[25] T. V. Vepkhvadze, ?On a formula of Ya. V. Uspenskii,? Soobshch. Akad. Nauk Gruz. SSR,46, No. 2, 301?308 (1967).
[26] T. V. Vepkhvadze, ?On the representation of numbers by certain binary quadratic forms,? Tr. Tbilis. Univ.,A1 (137), 17?24 (1971).
[27] T. V. Vepkhvadze, ?On the representation of numbers by certain quadratic forms with six variables,? Tr. Tbilis. Mat. Inst. Akad. Nauk Gruz. SSR,40, 5?20 (1971).
[28] T. V. Vepkhvadze, ?On the representation of numbers by positive Gaussian binary quadratic forms,? Tr. Tbilis. Mat. Inst. Akad. Nauk Gruz. SSR,40, 21?58 (1971).
[29] T. V. Vepkhvadze, ?On the representation of numbers by positive binary quadratic forms of odd discriminant,? Tr. Tbilis. Mat. Inst. Akad. Nauk Gruz. SSR,45, 5?40 (1974). · Zbl 0231.10014
[30] T. V. Vepkhvadze, ?On the number of representations of numbers by certain quaternary quadratic forms,? Tr. Tbilis. Mat. Inst. Akad. Nauk Gruz. SSR,45, 41?59 (1974).
[31] A. I. Vinogradov, ?On the extendability to the left half plane of the scalar product of Hecke L-series with characters of magnitude,? Izv. Akad. Nauk SSSR, Ser. Mat.,29, No. 2, 485?492 (1965).
[32] A. I. Vinogradov, ?Kubota series and theta functions,? in: Current Problems of Analytic Number Theory [in Russian], Nauka i Tekhnika, Minsk (1974), pp. 23?48.
[33] A. B. Voronetskii, ?Eisenstein series of weight-3/2 and singular Hardy-Littlewood series for ternary quadratic forms,? Zap. Nauch. Sem. Leningr. Otd. Mat. Inst.,50, 156?168 (1975).
[34] A. B. Voronetskii and A. V. Malyshev, ?On a simultaneous representation of a pair of numbers by sums of integers and their squares,? Tr. Mat. Inst. Akad. Nauk SSSR,142, 122?134 (1976).
[35] E. Gaigalas. ?On the scalar product of Hecke L-series of quadratic fields,? Lit. Mat. Sb.,15, No. 4, 41?52 (1976). · Zbl 0346.12008
[36] É. Gaigalas, ?On the scalar product of the Hecke L-series of some algebraic fields,? Lit. Mat. Sb.,17, No. 1, 65?74 (1977). · Zbl 0391.12007
[37] G. P. Gogishvili, ?On the number of representations of numbers by certain quaternary quadratic forms,? Soobshch. Akad. Nauk Gruz. SSR,56, No. 3, 525?528 (1969).
[38] G. P. Gogishvili, ?On the number of representations of numbers by positive quaternary diagonal quadratic forms,? Soobshch. Akad. Nauk Gruz. SSR,59, No. 3, 537?540 (1970).
[39] G. P. Gogishvili, ?On the summation of a singular series connected with diagonal quadratic forms with four variables,? Tr. Tbilis. Mat. Inst. Akad. Nauk Gruz. SSR,38, 5?30 (1970).
[40] G. P. Gogishvili, ?On the number of representations of numbers by positive quaternary diagonal quadratic forms,? Tr. Tbilis. Mat. Inst. Akad. Nauk Gruz. SSR,40, 59?105 (1971).
[41] G. P. Gogishvili, ?On the finiteness of the number of determinate classes of positive primitive quadratic forms,? Tr. Tbilis. Mat. Inst. Akad. Nauk Gruz. SSR,45, 78?110 (1974).
[42] E. P. Golubeva and O. M. Fomenko, ?On the series ?F(m)qm, where F(m) is the number of odd classes of binary quadratic forms of determinant-m,? Zap. Nauch. Sem. Leningr. Otd. Mat. Inst. Akad. Nauk SSSR,64, 69?79 (1976). · Zbl 0341.10023
[43] R. Sh. Gongadze, ?On the representation of numbers by certain quadratic forms with four variables,? Soobshch. Akad. Nauk Gruz. SSR,28, No. 4, 385?392 (1962).
[44] R. Sh. Gongadze, ?On the representation of numbers by the forms x2+3y2+4z2+12t2 and x2+2y2+32z2+32t2,? Soobshch. Akad. Nauk Gruz. SSR,46, No. 1, 22?40 (1967).
[45] R. Sh. Gongadze, ?On the representation of numbers by certain forms of the form x2+22k+1y2+32z2+32t2,? Soobshch. Akad. Nauk Gruz. SSR,50, No. 3, 519?524 (1968).
[46] V. L. Kalinin, ?An explicit formula for the trace of Brandt matrices,? Zap. Nauch. Sem. Leningr. Otd. Mat. Inst. Akad. Nauk SSSR,63, 67?94 (1976). · Zbl 0367.10018
[47] V. G. Kats, ?Infinite-dimensional Lie algebras and the Dedekind ?-function,? Funkts. Anal. Prilozhen.,8, 77?78 (1974). · Zbl 0298.57019 · doi:10.1007/BF02028317
[48] B. Kh. Kirshtein, ?On a property of modular functions constructed by means of a discriminant,? Usp. Mat. Nauk,29, No. 5, 227 (1974).
[49] B. Kh. Kirshtein and I. I. Pyatetskii-Shapiro, ?Invariant subrings of induced rings,? Izv. Akad. Nauk SSSR, Ser. Mat.,34, No. 1, 83?89 (1970).
[50] A. A. Kiselev, ?On the number of classes of ideals in cubic fields,? Uch. Zap. Leningr. Gos. Pedagog. Inst.,14, 46?51 (1955).
[51] L. A. Kogan, ?The theory of modular forms and the problem of finding formulas for the number of representations of numbers by positive quadratic forms,? Dokl. Akad. Nauk SSSR,182, No. 2, 259?261 (1968). · Zbl 0194.35103
[52] L. A. Kogan, ?The Liouville formulas and parabolic forms generated by generalized binary theta series,? Lit. Mat. Sb.,9, No. 3, 519?533 (1969).
[53] L. A. Kogan, On the Representation of Integers by Positive Definite Quadratic Forms [in Russian], Fan, Tashkent (1971). · Zbl 0227.10015
[54] L. A. Kogan, ?The conjecture of I. M. Vinogradov on the least square residue and the representation of numbers by quadratic forms,? Dokl. Akad. Nauk SSSR,198, No. 6, 1263?1264 (1971).
[55] L. A. Kogan, ?Elliptic curves and modular forms,? Dokl. Akad. Nauk SSSR,204, No. 2, 275?278(1972). · Zbl 0269.10015
[56] L. A. Kogan, ?On a generalization of a conjecture of A. Weil and the representationof theta series by Eisenstein series and generalized binary theta series,? Uch. Zap. Tashk. Gos. Pedagog. Inst.,163, 3?45 (1976). · Zbl 0447.10026
[57] L. A. Kogan and A. Mirsalikhov, ?On the representability of theta series by Eisenstein series,? Dokl. Akad. Nauk Uzb. SSR, No. 2, 6?7 (1971). · Zbl 0234.10016
[58] L. A. Kogan and A. Mirsalikhov, ?On the representability of theta series by Eisenstein series,? Izv. Akad. Nauk Uzb. SSR, Ser. Fiz.-Mat. Nauk, No. 1, 23?27 (1972).
[59] L. A. Kogan and A. Mirsalikhov, ?On the representability of the Fourier coefficients of theta series by the sum of the singular Hardy-Littlewood series and the Fourier coefficients of generalized binary theta series,? Uch. Zap. Tashk. Pedagog. Inst.,163, 46?60 (1976). · Zbl 0449.10020
[60] L. A. Kogan and A. Sagintaev, ?Modular forms and quadratic forms with six variables,? Dokl. Akad. Nauk Uzb. SSR, No. 1, 3?4 (1972).
[61] N. S. Koshlyakov, ?Investigation of some questions of the analytic theory of rational and quadratic fields. I, II, III,? Izv. Akad. Nauk SSSR, Ser. Mat.,18, No. 2, 113?144; No. 3, 212?260; No. 4, 307?326 (1954).
[62] V. A. Krechmar, ?On some division properties of an additive function,? Izv. Akad. Nauk, OMEN,6, No. 6, 763?800 (1933).
[63] N. V. Kuznetsov, ?A new class of identities for the Fourier coefficients of modular forms,? Acta Arithm.,27, 505?519 (1975).
[64] B. V. Levin, ?On a nonlinear differential operator connected with automorphic functions,? Inst. Mat. Mekh. Akad. Nauk Uzb. SSR, No. 18, 129?138 (1956).
[65] B. V. Levin, ?On a special class of differential operators connected with the theory of modular functions and number theory,? Tr. Third All-Union Mathematical Congress,1, Akad. Nauk SSSR, Moscow (1956), pp. 6?7.
[66] B. V. Levin, ?New congruences for the Ramanujan function?(n),? Uch. Zap. Tashk. Gos. Pedagog. Inst., No. 7, 5?8 (1957).
[67] B. V. Kogan, ?Exact formulas for the number of representations of certain numbers by the quadratic forms x2+y2+5(z2+t2) and x2+y2+7(z2+t2),? Uch. Zap. Tashk. Gos. Pedagog. Inst., No. 7, 23?24 (1957).
[68] K. L. Leibson, ?On integer points inside ellipsoids in connection with the theory of Hecke operators,? Vestn. Leningr. Univ., No. 1, 153?155 (1965).
[69] G. A. Lomadze, ?On the representation of numbers by sums of squares,? Tr. Tbilis. Mat. Inst.,16, 231?275 (1948).
[70] G. A. Lomadze, ?On the representation of numbers by sums of an odd number of squares,? Tr. Tbilis. Mat. Inst.,17, 281?314 (1949).
[71] G. A. Lomadze, ?On the representation of numbers by sums of squares,? Tr. Tbilis. Mat. Inst.,20, 47?87 (1954).
[72] G. A. Lomadze, ?On the representation of numbers by sums of generalized polygonal numbers. I, II,? Tr. Tbilis. Mat. Inst.,22, 77?102 (1956);24, 3?33 (1957). · Zbl 0075.03301
[73] G. A. Lomadze, ?On the representation of numbers by sums of generalized polygonal numbers,? Tr. Tbilis. Univ.,64, 81?91 (1957).
[74] G. A. Lomadze, ?On the representation of numbers by certain quadratic forms with four variables,? Tr. Tbilis. Univ.,76, 107?159 (1959).
[75] G. A. Lomadze, ?On the representation of numbers by binary quadratic forms,? Tr. Tbilis. Univ.,84, 285?290 (1961).
[76] G. A. Lomadze, ?On the representation of numbers by positive binary diagonal quadratic forms,? Mat. Sb.,68, No. 2, 282?312 (1965).
[77] G. A. Lomadze, ?On the representation of numbers by certain quaternary quadratic forms,? Tr. Tbilis. Univ.,110, 163?180 (1965).
[78] G. A. Lomadze, ?On the representation of numbers by certain quadratic forms with six variables. I, II,? Tr. Tbilis. Univ.,117, 7?43 (1966);129, 279?297 (1968).
[79] G. A. Lomadze, ?On the representation of numbers by certain binary quadratic forms,? Izv. Vyssh. Uchebn. Zaved., Mat., No. 11, 71?75 (1970).
[80] G. A. Lomadze, ?On the number of representations of numbers by quadratic forms with four variables,? Tr. Tbilis. Mat. Inst. Akad. Nauk Gruz. SSR,40, 106?139 (1971).
[81] G. A. Lomadze, ?Formulas for the number of representations of numbers by all primitive positive ternary diagonal quadratic forms belonging to single-class type,? Tr. Tbilis. Mat. Inst. Akad. Nauk Gruz. SSR,40, 140?179 (1971).
[82] G. A. Lomadze, ?On the representation of numbers by positive ternary diagonal quadratic forms. I, II,? Acta Arithm.,19, No. 3, 267?305 (1971). · Zbl 0233.10011
[83] G. A. Lomadze, ?On the behavior of derivatives of theta functions under linear substitutions,? Tr. Tbilis. Univ.,A4(146), 15?27 (1972).
[84] G. A. Lomadze, ?On a basis of the space of spherical functions of fourth order relative to a positive quadratic form,? Tr. Tbilis. Mat. Inst., Akad. Nauk Gruz. SSR,69, No. 3, 533?536 (1973). · Zbl 0258.10007
[85] G. A. Lomadze, ?On a basis of the space of spherical functions relative to a positive quadratic form,? Tr. Tbilis. Mat. Inst. Akad. Nauk Gruz. SSR,45, 134?145 (1974).
[86] G. A. Lomadze, ?On parabolic forms of prime level and principal type. I,? Tr. Tbilis. Mat. Inst. Akad. Nauk Gruz. SSR,45, 146?161 (1974).
[87] G. A. Lomadze, ?On the number of representations of numbers by positive quadratic forms with six variables,? Tr. Tbilis. Mat. Inst. Akad. Nauk Gruz. SSR,45, 111?133 (1974).
[88] G. A. Lomadze, ?Formulas for the number of representations of numbers by certain regular and semiregular ternary quadratic forms belonging to double-class type,? Acta Arithm.
[89] A. V. Malyshev, ?On the representation of integers by positive quadratic forms,? Tr. Mat. Inst. Akad. Nauk SSSR,65 (1962).
[90] A. V. Malyshev, ?On the Fourier coefficients of modular forms (remarks on the paper ’Generalized Kloosterman sums and their estimates’),? Zap. Nauch. Seminarov Leningr. Otd. Mat. Inst. Akad. Nauk SSSR,1, 140?163 (1966).
[91] A. V. Malyshev, ?On formulas for the number of representations of numbers by positive quadratic forms (problematics),? in: Current Problems of Analytic Number Theory [in Russian], Nauka i Tekh., Minsk (1974), pp. 119?137.
[92] Yu. I. Manin, ?Cyclic fields and modular fields,? Usp. Mat. Nauk,26, No. 6, 7?71 (1971).
[93] Yu. I. Manin, ?Parabolic points and zeta functions of modular curves,? Izv. Akad. Nauk SSSR, Ser. Mat.,36, No. 1, 19?66 (1972).
[94] Yu. I. Manin, ?Periods of parabolic forms and p-adic Hecke series,? Mat. Sb.,92, No. 3, 378?401 (1973).
[95] Yu. I. Manin, ?p-Adic automorphic functions,? in: Sovrem. Probl. Mat., Vol. 3 (Itogi Nauki i Tekh., VINITI Akad. Nauk SSSR), Moscow (1974), pp. 5?92.
[96] A. Mirsalikhov, ?The theory of modular forms and the problem of finding formulas for the number of representations of numbers by positive quadratic forms with six variables,? Izv. Akad. Nauk Uzb. SSR, Ser. Fiz.-Mat. Nauk, No. 1, 7?10 (1971). · Zbl 0233.10015
[97] B. Z. Moroz, ?On zeta functions of fields of algebraic numbers,? Mat. Zametki,4, No. 3, 333?339 (1968). · Zbl 0167.04303
[98] A. P. Novikov, ?On the number of classes of fields of complex multiplication,? Izv. Akad. Nauk SSSR, Ser. Mat.,26, No. 5, 677?686 (1962).
[99] A. P. Novikov, ?On the number of classes of fields Abelian over an imaginary quadratic field,? Izv. Akad. Nauk SSSR, Ser. Mat.,31, No. 3, 717?726 (1967).
[100] M. E. Novodvorskii, ?On some fixed vectors in infinite-dimensional representations of Chevalier groups,? Funkts. Anal. Prilozhen.,5, No. 1, 87?88 (1971).
[101] M. E. Novodvorskii, ?On some subspaces in the representations of groups of matrices of second order with coefficients from a locally compact, nonconnected field,? Mat. Sb.,88, No. 3, 360?375 (1972).
[102] A. A. Panchishkin, ?Ramanujan congruences mod 6912 do not exist,? Mat. Zametki,17, No. 2, 255?264 (1975).
[103] I. I. Pyatetskii-Shapiro, ?The theory of modular functions and related questions of the theory of discrete groups,? Usp. Mat. Nauk,15, No. 1, 99?136 (1960).
[104] I. I. Pyatetskii-Shapiro, ?On the reduction by prime modulus of fields of modular functions,? Izv. Akad. Nauk SSSR, Ser. Mat.,32, No. 6, 1264?1274 (1968).
[105] I. V. Reshetukha, ?A question in the theory of cubic residues,? Mat. Zametki,7, No. 4, 469?476 (1970). · Zbl 0194.35007
[106] A. Sagintaev, ?Modular forms and formulas of Bulygin-Mordell type,? Izv. Akad. Nauk Uzb. SSR, Ser. Fiz.-Mat. Nauk, No. 6, 31?33 (1971).
[107] A. Sagintaev, ?Modular forms and formulas of Bulygin-Mordell type,? Nauch. Zap. Tashk. Inst. Nar. Khva., No. 60, 118?129 (1971). · Zbl 0234.10018
[108] A. Sagintaev, ?Modular and quadratic forms with six variables,? Izv. Akad. Nauk Uzb. SSR, Ser. Fiz.-Mat. Nauk, No. 3, 96?98 (1973).
[109] T. V. Fedorova, ?The representation of numbers by some quadratic forms with four variables,? Nauch. Zap. Tashk. Inst. Nar. Khva., No. 55, 137?142 (1970).
[110] T. V. Fedorova and L. A. Kogan, ?On the Fourier coefficients of some parabolic forms,? Sb. Tr. Tashk. Inst. Inzh. Zh.-D. Trans., No. 56, 93?97 (1968).
[111] O. M. Fomenko, ?Estimates of the Petersson inner product with application to the theory of quaternary quadratic forms,? Dokl. Akad. Nauk SSSR,152, No. 3, 559?562 (1963). · Zbl 0128.27203
[112] O. M. Fomenko, ?On the Fourier coefficients of Poincare series of dimension-2,? Dokl. Akad. Nauk SSSR,153, No. 6, 1273?1275 (1963).
[113] O. M. Fomenko, ?On the representation of parabolic forms by theta series,? Dokl. Akad. Nauk SSSR,166, No. 3, 555?557 (1966). · Zbl 0199.08903
[114] O. M. Fomenko, ?The trace formula for the Hecke operator in the space of parabolic forms relative to a principal congruence subgroup,? Izv. Akad. Nauk Uzb. SSR, Ser. Fiz.-Mat. Nauk, No. 1, 26?28 (1968).
[115] O. M. Fomenko, ?Application of Eichler’s reduction formula to the representation of numbers by certain quaternary quadratic forms,? Mat. Zametki,9, No. 1, 71?76 (1971). · Zbl 0223.10008
[116] O. M. Fomenko, ?Extendability to the entire plane and the functional equation of the scalar product of Hecke L-series of two quadratic fields,? Tr. Mat. Inst. Akad. Nauk SSSR,128, 232?241 (1972).
[117] O. M. Fomenko, ?The distribution of values of the Ramanujan functions?,? Reports to the All-Union Conference: Problems of Analytic Number Theory and Its Applications, Vilnius (1974), pp. 231?232.
[118] H.-F. Aas, ?Congruences for the coefficients of the modular invariant j(?),? Math. Scand.,14, No. 2, 185?192 (1964). · Zbl 0144.27506 · doi:10.7146/math.scand.a-10717
[119] H.-F. Aas, ?Congruences for the coefficients of the modular invariant j(?),? Math. Scand.,15, No. 1, 64?68 (1964). · Zbl 0135.09105 · doi:10.7146/math.scand.a-10727
[120] T. M. Apostol, Modular Functions and Dirichlet Series in Number Theory, Graduate Texts in Mathematics, Vol. 43, Springer-Verlag, New York (1976).
[121] Tetsuya Asai, ?The resiprocity of Dedekind sums and the factor set for the universal covering group of SL(2, R),? Nagoya Math. J.,37, 67?80 (1970). · Zbl 0192.39601 · doi:10.1017/S0027763000013301
[122] Tetsuya Asai, ?On a certain function analogous to log ?(z)|,? Nagoya Math. J.,40, 193?211 (1970). · Zbl 0213.05701 · doi:10.1017/S0027763000013957
[123] Tetsuya Asai, ?On a certain modular function corresponding to a real cyclotomic field,? Seminar on Modern Methods in Number Theory (Inst. Statist. Math., Tokyo, 1971), Paper No. 9, Inst. Statist. Math., Tokyo (1971).
[124] Tetsuya Asai, ?On the Fourier coefficients of automorphic forms at various cusps and some applications to Rankin’s convolution,? J. Math. Soc. Jpn.,28, No. 1, 48?61 (1976). · Zbl 0313.10026 · doi:10.2969/jmsj/02810048
[125] A. G. van Asch, ?Modular forms and root systems,? Math. Ann.,222, No. 2, 145?170 (1976). · Zbl 0329.10017 · doi:10.1007/BF01418325
[126] B. van Asch, ?Des identites pour certaines puissances de ?,? C. R. Acad. Sci.,277, No. 22, A1087-A1090 (1973). · Zbl 0268.10011
[127] A. O. L. Atkin, ?Proof of a conjecture of Ramanujan,? Glasgow Math.,8, No. 1, 14?32 (1967). · Zbl 0163.04302 · doi:10.1017/S0017089500000045
[128] A. O. L. Atkin, ?Note on a paper of Birch,? J. London Math. Soc.,44, No. 2, 282 (1968).
[129] A. O. L. Atkin, ?Multiplicative congruence properties and density problems for p(n),? Proc. London Math. Soc.,18, No. 3, 563?576 (1968). · Zbl 0313.10025 · doi:10.1112/plms/s3-18.3.563
[130] A. O. L. Atkin, ?Congruences for modular forms,? in: Computers in Mathematical Research, R. F. Churchhouse and J. C. Herz (eds.), North Holland, Amsterdam (1968), pp. 8?19.
[131] A. O. L. Atkin, ?Congruence Hecke operators,? Proc. Sympos. Pure Math., Vol. 12, Number Theory, Providence, R. I. (1969), pp. 33?40. · doi:10.1090/pspum/012/9990
[132] A. O. L. Atkin, ?Note on a paper of Rankin,? Bull. London Math. Soc.,1, No. 2, 191?192 (1969). · Zbl 0179.35001 · doi:10.1112/blms/1.2.191
[133] A. O. L. Atkin and J. N. O’Brien, ?Some properties of p(n) and c(n) modulo powers of 13,? Trans. Am. Math. Soc.,126, No. 3, 442?459 (1967).
[134] A. O. L. Afckin and J. Lehner, ?Hecke operators on ?0(m),? Math. Ann.,185, No. 2, 134?160 (1970). · Zbl 0177.34901 · doi:10.1007/BF01359701
[135] A. O. L. Atkin and H. P. F. Swinnerton-Dyer, ?Some properties of partitions,? Proc. London Math. Soc.,4, No. 13, 84?106 (1954). · Zbl 0055.03805 · doi:10.1112/plms/s3-4.1.84
[136] A. O. L. Atkin and H. P. F. Swinnerton-Dyer, ?Modular forms on noncongruence subgroups,? in: Proc Sympos. Pure Math., Vol. 19, Combinatorics, Providence, R. I. (1971), pp. 1?25. · Zbl 0235.10015
[137] A. Baker, ?Linear forms in the logarithms of algebraic numbers,? Matematika,13, No. 2, 204?216 (1966). · Zbl 0161.05201 · doi:10.1112/S0025579300003971
[138] A. Baker, ?Imaginary quadratic fields with class number 2,? Ann. Math.,94, No. 1, 139?152 (1971). · Zbl 0219.12008 · doi:10.2307/1970739
[139] K. Barner, ?Über die Werte der Ringklassen-L-Funktionen reellquadratischer Zahlkörper an natürlichen Argumentstellen,? J. Number Theory,1, No. 1, 28?64 (1969). · Zbl 0174.08604 · doi:10.1016/0022-314X(69)90024-9
[140] P. Barrucand, ?Sur certaines fonctions a caractere arithmetique,? C. R. Acad. Sci.,249, No. 21, 2146?2148 (1959).
[141] P. Barrucand, ?Sur une formule de Selberg et Chowla,? C. R. Acad. Sci.,268, No. 23, A1398?1401 (1969). · Zbl 0279.10032
[142] P. Barrucand, ?Sur certaines series de Dirichlet,? C. R. Acad. Sci.,269, No. 7, A294-A296 (1969). · Zbl 0204.37102
[143] P. Barrucand, ?Quelques proprietes des coefficients des series L associees aux corps cubiques,? C. R. Acad. Sci.,273, No. 21, A960-A963 (1971). · Zbl 0236.12009
[144] P. T. Bateman, ?On the representations of a number as the sum of three squares,? Trans. Am. Math. Soc.,71, No. 1, 70?101 (1951). · doi:10.1090/S0002-9947-1951-0042438-4
[145] P. T. Bateman and E. Grosswald, ?On Epstein’s zeta function,? Acta Arithm.,9, No. 4, 365?373 (1964). · Zbl 0128.27004
[146] B. C. Berndt, ?Identities involving the coefficients of a class of Dirichlet series. I, II, III, IV, V, VI, VII,? Trans. Am. Math. Soc.,137, 345?359, 361?374 (1969);146, 323?348 (1970);149, 179?185 (1970);160, 139?156, 157?167 (1971);201, 247?261 (1975). · Zbl 0175.32802 · doi:10.2307/1994808
[147] B. C. Berndt, ?On the average order of some arithmetical functions,? Bull. Am. Math. Soc.,76, No. 4, 856?859 (1970). · Zbl 0197.32101 · doi:10.1090/S0002-9904-1970-12585-X
[148] B. C. Berndt, ?The Voronoi summation formula,? Lect. Notes Math.,251, 21?36 (1972). · Zbl 0228.10023 · doi:10.1007/BFb0058783
[149] B. C. Berndt, ?Generalized Dedekind sums,? Trans. Am. Math. Soc.,178, 495?508 (1973). · Zbl 0262.10015 · doi:10.1090/S0002-9947-1973-0371817-5
[150] B. C. Berndt, ?Character transformation formulae similar to those for the Dedekind eta function,? Proc. Symp. Pure Math., Vol. 24, Analytical Number Theory, Providence, R. I. (1973), pp. 9?30. · Zbl 0265.10016 · doi:10.1090/pspum/024/0337787
[151] B. C. Berndt, ?Generalized Eisenstein series and modified Dedekind sums,? J. Reine Angew. Math.,272, 182?193 (1975). · Zbl 0294.10018
[152] B. C. Berndt, ?On Eisenstein series with characters and the values of Dirichlet L-functions,? Acta Arithm.,28, No. 3, 299?320 (1975).
[153] B. C. Berndt, ?Dedekind sums and a paper of G. H. Hardy,? J. London Math. Soc,13, No. 1, 129?137 (1976). · Zbl 0319.10006 · doi:10.1112/jlms/s2-13.1.129
[154] B. J. Birch, ?How the number of points of an elliptic curve over a fixed prime field varies,? J. London Math. Soc,43, No. 1, 57?60 (1968). · Zbl 0183.25503 · doi:10.1112/jlms/s1-43.1.57
[155] B. J. Birch, ?Weber’s class invariants,? Mathematika,16, No. 2, 283?294 (1969). · Zbl 0226.12005 · doi:10.1112/S0025579300008251
[156] B. J. Birch, ?Diophantine analysis and modular functions,? Algebr. Geom. London, 35?42 (1969).
[157] B. J. Birch, ?Elliptic curves and modular functions,? in: Sympos. Math., Vol. 4, London-New York (1970), pp. 27?32.
[158] B. J. Birch, ?Some calculations of modular relations,? Lect. Notes Math.,320, 175?186 (1973). · Zbl 0261.10019 · doi:10.1007/978-3-540-38509-7_6
[159] B. J. Birch, ?Heegner points of elliptic curves,? Symp. Math. Ist. Naz. Alta Mat., Vol. 15, London-New York (1975), pp. 441?445.
[160] B. J. Birch, ?A look back at Ramanujan’s notebooks,? Math. Proc. Cambr. Phil. Soc,78, No. 1, 73?79 (1975). · Zbl 0305.10002 · doi:10.1017/S0305004100051501
[161] F. van der Blij, ?Even quadratic forms with determinant unity,? Quart. J. Math.,5, No. 20, 297?300 (1954). · Zbl 0057.04002 · doi:10.1093/qmath/5.1.297
[162] F. van der Blij, ?Quadratic forms and Euler products,? Proc. K. Ned. Akad. Wet., Ser. A,59, No. 2, 229?237 (1956); Indag. Math.,18, No. 2, 229?237 (1956).
[163] F. van der Blij, ?The value of a certain Epstein zeta function,? Nieuw Arch. Wisk.,4, No. 1, 13?14 (1956). · Zbl 0071.06701
[164] F. van der Blij, ?Simultaneous representation of integers by a quadratic and a linear form,? Nieuw Arch. Wisk.,7, No. 3, 109?114 (1959). · Zbl 0089.26704
[165] F. van der Blij and J. H. van Lint, ?On some special theta functions,? Proc. K. Ned. Akad. Wet.,A61, No. 5, 508?513 (1958). · Zbl 0083.07302
[166] R. Bodendiek and U. Halbritter, ?Über die Transformationsformel von log ?(?) und gewisser Lambertscher Reihen,? Abh. Math. Semin. Univ. Hamburg,38, 147?167 (1972). · Zbl 0236.10016 · doi:10.1007/BF02996930
[167] A. Borel, ?Operateurs de Hecke et fonctions zeta,? Semin. Bourbaki, 18 annee, No. 307 (1965/1966).
[168] A. Borel, ?Formes automorphes et series de Dirichlet (d’apres R. P. Langlands),? Lect. Notes Math.,514, 183?222 (1976). · Zbl 0329.10019 · doi:10.1007/BFb0080067
[169] L. de Branges, ?The Riemann hypothesis for modular forms,? J. Math. Anal. Appl.,35, No. 2, 285?311 (1971). · Zbl 0188.34605 · doi:10.1016/0022-247X(71)90220-4
[170] L. de Branges, ?Coefficients of modular forms,? J. Math. Anal. Appl.,45, No. 2, 300?323 (1974). · Zbl 0283.10011 · doi:10.1016/0022-247X(74)90074-2
[171] L. de Branges, ?Examples of modular forms,? J. Math. Anal. Appl.,46, No. 2, 358?368 (1974). · Zbl 0294.10017 · doi:10.1016/0022-247X(74)90246-7
[172] K. Burde, ?Dedekindsummen als Gitterpuktzahlen,? J. Reine Angew. Math.,227, 74?85 (1967).
[173] R. Busam, ?Eine Verallgemeinerung gewisser Dimensionsformeln von Shimizu,? Invent. Math.,11, No. 2, 110?149 (1970). · Zbl 0202.36802 · doi:10.1007/BF01404607
[174] L. Carlitz, ?Note on some paritition formulae,? Q. J. Math.,4, No. 15, 168?172 (1953). · Zbl 0053.02602 · doi:10.1093/qmath/4.1.168
[175] L. Carlitz, ?The coefficients of singular elliptic functions,? Math. Ann.,127, No. 2, 162?169 (1954). · Zbl 0055.27004 · doi:10.1007/BF01361117
[176] L. Carlitz, ?Note on the multiplication formulas for the Jacobi elliptic functions,? Pac. J. Math.,5, No. 2, 169?176 (1955). · Zbl 0058.27306 · doi:10.2140/pjm.1955.5.169
[177] L. Carlitz, ?On the representation of an integer as the sum of twenty-four squares,? Proc. K. Ned. Akad. Wet.,A58, No. 4, 504?506 (1955). · Zbl 0068.04001
[178] L. Carlitz, ?Note on sums of four and six squares,? Proc. Am. Math. Soc.,8, No. 1, 120?124 (1957). · Zbl 0079.06505 · doi:10.1090/S0002-9939-1957-0084520-2
[179] L. Carlitz, ?A congruence satisfied by the theta constant? 3,? Proc. Am. Math. Soc,10, No. 6, 912?916 (1959). · Zbl 0095.26203
[180] L. Carlitz, ?Congruences (mod 2r) for the coefficients of the Jacobi elliptic functions,? Math. Z.,72, No. 4, 307?318 (1960). · Zbl 0098.03703 · doi:10.1007/BF01162956
[181] L. Carlitz, ?Generalized Dedekind sums,? Math. Z.,85, No. 1, 83?90 (1964). · Zbl 0122.05104 · doi:10.1007/BF01114880
[182] L. Carlitz, ?Linear relations among generalized Dedekind sums,? J. Reine Angew. Math.,220, Nos. 3?4, 154?162 (1965). · Zbl 0148.27305
[183] L. Carlitz, ?Generating functions and partition problems,? in: Proc. Symp. Pure Math., Vol. 8, Theory of Numbers, Am. Math. Soc., Providence, R. I. (1965), pp. 144?169. · Zbl 0142.25104
[184] L. Carlitz, ?Inversions and generalized Dedekind sums,? Abh. Math. Semin. Univ. Hamburg,42, Nov., 41?52 (1974). · Zbl 0292.10007 · doi:10.1007/BF02993536
[185] L. Carlitz, ?A reciprocity and four-term relation for generalized Dedekind sums,? Proc. K. Ned. Akad. Wet.,A77, No. 5, 413?422 (1974); Indag. Math.,36, No. 5, 413?422 (1974). · Zbl 0291.10005
[186] L. Carlitz, ?A three-term relation for some sums related to Dedekind sums,? Pac. J. Math.,57, No. 2, 339?348 (1975). · Zbl 0311.10006 · doi:10.2140/pjm.1975.57.339
[187] L. Carlitz, ?The reciprocity theorem for Dedekind-Rademacher sums,? Acta Arithm.,29, No. 3, 309?313 (1976). · Zbl 0282.10016
[188] H. Cartan, ?Formes modulaires,? in: Semin. H. Cartan, Ecole Norm. Super., 1957?1958, I, Paris (1958), 4-1?4-12.
[189] P. Cartier, ?Groupes formels, fonctions automorphes et fonctions zeta des courbes elliptiques,? in: Actes Congr. Int. Mathematiciens, 1970, Vol. 2, Paris (1971), pp. 291?299.
[190] W. Casselman, ?On some results of Atkin and Lehner,? Math. Ann.,201, No. 4, 301?314 (1973). · Zbl 0239.10015 · doi:10.1007/BF01428197
[191] J. W. S. Cassels, ?On Kummer sums,? Proc. London Math. Soc.,21, No. 1, 19?27 (1970). · Zbl 0197.32004 · doi:10.1112/plms/s3-21.1.19
[192] J. W. S. Cassels, ?Some elliptic function identities,? Acta Arithm.,18, 37?52 (1971). · Zbl 0218.14016
[193] K. Chandrasekharan and R. Narasimhan, ?Hecke’s functional equation and arithmetical identities,? Ann. Math.,74, No. 1, 1?23 (1961). · Zbl 0107.03702 · doi:10.2307/1970304
[194] K. Chandrasekharan and R. Narasimhan, ?Functional equations with multiple gamma factors and the average order of arithmetical functions,? Ann. Math.,76, No. 1, 93?136 (1962). · Zbl 0211.37901 · doi:10.2307/1970267
[195] K. Chandrasekharan and R. Narasimhan, ?The approximate functional equation for a class of zeta functions,? Math. Ann.,152, No. 1, 30?64 (1963). · Zbl 0116.27001 · doi:10.1007/BF01343729
[196] S. Chowla, ?The Riemann hypothesis and Hilbert’s tenth problem,? Gordon and Breach, New York (1965). · Zbl 0136.32702
[197] S. Chowla, ?Stark’s series expressed by theta functions,? Kgl. Norske Vid. Selskabs Forhandl,40, No.7, 31?33 (1967). · Zbl 0166.31002
[198] S. Chowla, ?Observation on a theorem of Stark,? Kgl. Norske Vid. Selskabs Forhandl.,40, No. 7, 31?33 (1967).
[199] S. Chowla, ?The Heegner-Stark-Baker-Deuring-Siegel theorem,? J. Reine Angew. Math.,241, 47?48 (1970). · Zbl 0205.35402
[200] H. Cohen, ?Sommes de carres, fonctions L et formes modulaires,? C. R. Acad. Sci.,277, No. 17, A827-A830 (1973). · Zbl 0267.10066
[201] H. Cohen, ?Variations sur un theme de Siegel-Hecke,? Semin. Delange-Pisot-Poitou, Theor. Nombres, Univ. Pierre et Marie Curie, 1973?1974,15, No. 1, 14/1?14/7 (1975).
[202] H. Cohen, ?Sums involving the values at negative integers of L-functions of quadratic characters,? Mat. Ann.,217, No. 3, 271?285 (1975). · Zbl 0311.10030 · doi:10.1007/BF01436180
[203] H. Cohen, ?Formes modulaires a deux variables associees a une forme a une variable,? C. R. Acad. Sci.,281, No. 18, A753-A755 (1975). · Zbl 0314.10020
[204] H. Cohen, ?Variations sur un theme de Siegel et Hecke,? Acta Arithm.,30, No. 1, 63?93 (1976). · Zbl 0291.10021
[205] H. Cohn, ?Approach to Markoff’s minimal forms through modular functions,? Ann. Math.,61, No. 1, 1?12 (1955). · Zbl 0064.04303 · doi:10.2307/1969618
[206] H. Cohn, ?Some algebraic number theory estimates based on the Dedekind eta function,? Am. J. Math.,78, No. 4, 791?796 (1956). · Zbl 0074.26501 · doi:10.2307/2372468
[207] H. Cohn, ?A numerical study of Dedekind’s cubic class number formula,? J. Res. Nat. Bur. Stand.,59, No. 4, 265?271 (1957). · Zbl 0122.04304 · doi:10.6028/jres.059.031
[208] H. Cohn, ?Numerical study of the representation of a totally positive quadratic integer as the sum of quadratic integral squares,? Numer. Math.,1, No. 3, 121?134 (1959). · Zbl 0092.27603 · doi:10.1007/BF01386378
[209] H. Cohn, ?Decomposition into four integral squares in the fields of 21/2 and 31/2,? Am. J. Math.,82, No. 2, 301?322 (1960). · Zbl 0097.03103 · doi:10.2307/2372737
[210] H. Cohn, ?Calculation of class numbers by decomposition into three integral squares in the fields of 21/2 and 31/2,? Am. J. Math.,83, No. 1, 33?56 (1961). · Zbl 0100.03201 · doi:10.2307/2372719
[211] H. Cohn, ?Cusp forms arising from Hilbert’s modular functions for the field of 31/2,? Am. J. Math.,84, No. 2, 283?305 (1962). · Zbl 0115.26503 · doi:10.2307/2372763
[212] H. Cohn, ?Some elementary aspects of modular functions in several variables,? Bull. Am. Math. Soc.,71, No. 5, 681?704 (1965). · Zbl 0163.32203 · doi:10.1090/S0002-9904-1965-11343-X
[213] H. Cohn, ?Representation of Markoff’s binary quadratic forms by geodesies on a perforated torus,? Acta Arithm.,18, 125?136 (1971). · Zbl 0218.10041
[214] H. Cohn, ?Markoff forms and primitive words,? Math. Ann.,196, No. 1, 8?22 (1972). · Zbl 0227.10018 · doi:10.1007/BF01419427
[215] H. Cohn, ?Some direct limits of primitive homotopy words and of Markoff geodesics,? Ann. Math. Stud., No. 79, 81?98 (1974). · Zbl 0294.20044
[216] P. Deligne, ?Formes modulaires et representationsl-adiques,? Lect. Notes Math.,179, 139?172 (1971). · Zbl 0206.49901 · doi:10.1007/BFb0058810
[217] P. Deligne, ?Travaux de Shimura,? Lect. Notes Math.,244, 123?165 (1971). · doi:10.1007/BFb0058700
[218] P. Deligne, ?La conjecture de Weil. I,? Publ. Math. Inst. Hautes Etudes Sci.,43, 273?307 (1974). · Zbl 0287.14001 · doi:10.1007/BF02684373
[219] P. Deligne and J. -P. Serre, ?Formes modulaires de poids. I,? Ann. Sci. Ecole Norm. Super.,7, 507?530 (1974). · Zbl 0321.10026 · doi:10.24033/asens.1277
[220] M. Deuring, ?Imaginäre quadratische Zahlkörper mit der Klassenzahl Eins,? Invent. Math.,5, No. 3, 169?179 (1968). · Zbl 0155.38001 · doi:10.1007/BF01425548
[221] G. Dirdal, ?Asymptotic formulae for the coefficients of a class of modular forms,? Math. Scand.,31, No. 1, 237?247 (1972). · Zbl 0252.10021 · doi:10.7146/math.scand.a-11430
[222] G. Dirdal, ?Asymptotic formulae for the coefficients of certain modular forms on ?0(3),? Arb. Univ. Bergen Mat.-Naturvit. Ser., 1971, No. 3, 1?16 (1974).
[223] B. Ditters, ?Sur les congruences d’Atkin et de Swinnerton-Dyer,? C. R. Acad. Sci.,282, No. 19, A1131-A1134 (1976).
[224] Koji Doi and Hidehisa Naganuma, ?On the functional equation of certain Dirichlet series,? Invent. Math.,9, No. 1, 1?14 (1969). · Zbl 0182.54301 · doi:10.1007/BF01389886
[225] P. K. J. Draxl, ?L-Funktionen algebraischer Tori,? J. Number Theory,3, No. 4, 444?467 (1971). · Zbl 0231.12018 · doi:10.1016/0022-314X(71)90013-8
[226] B. Dwork, ?On Hecke polynomials,? Invent. Math.,12, No. 3, 249?256 (1971). · Zbl 0219.14014 · doi:10.1007/BF01418784
[227] B. Dwork, ?The Up operator of Atkin on modular functions of level 2 with growth conditions,? Lect. Notes Math.,350, 57?67 (1973). · Zbl 0276.14010 · doi:10.1007/978-3-540-37802-0_2
[228] F. Dyson, ?Missed opportunities,? Bull. Am. Math. Soc.,78, No. 5, 635?653 (1972). · Zbl 0271.01005 · doi:10.1090/S0002-9904-1972-12971-9
[229] M. Eichler, Quadratische Formen und Orthogonale Gruppen, Springer, Berlin-Gottingen-Heidelberg (1952).
[230] M. Eichler, ?Quaternäre quadratische Formen und die Riemannsche Vermutung für die Kongruenzzeta-funktion,? Arch. Math.,5, Nos. 4?6, 355?366 (1954). · Zbl 0059.03804 · doi:10.1007/BF01898377
[231] M. Eichler, ?Zur Zahlentheorie der Quaternionen-Algebren,? J. Reine Angew. Math.,195, Nos. 3?4, 127?151 (1955); errata: ibid.,197, Nos. 3?4, 220 (1957).
[232] M. Eichler, ?Über die Darstellbarkeit von Modulformen durch Thetareihen,? J. Reine Angew. Math.,195, Nos. 3?4, 156?171 (1955); errata: ibid.,196, Nos. 3?4, 155 (1956).
[233] M. Eichler, ?On the class number of imaginary quadratic fields and the sums of divisors of natural numbers,? J. Indian Math. Soc.,19, Nos. 3?4, 153?180 (1955). · Zbl 0068.03302
[234] M. Eichler, ?Eine Verallgemeinerung der Abelschen Integrale,? Math. Z.,67, No. 3, 267?298 (1957). · Zbl 0080.06003 · doi:10.1007/BF01258863
[235] M. Eichler, ?Modular correspondences and their representations,? J. Indian Math. Soc.,20, Nos. 1?3, 163?206 (1956). · Zbl 0073.26501
[236] M. Eichler, ?Quadratische Formen and Modulfunktionen,? Acta Arithm.,4, No. 3, 217?239 (1958). · Zbl 0086.06604
[237] M. Eichler, Einführung in die Theorie der Algebraischen Zahlen und Funktionen, Birkhäuser Verlag, Basel-Stuttgard (1963). · Zbl 0152.19501
[238] M. Eichler, ?Grenzkreisgruppen und kettenbruchartige Algorithmen,? Acta. Arithm.,11, No. 2, 169?180 (1965).
[239] M. Eichler, ?Einige Anwendungen der Spurformel im Bereich der Modularkorrespondenzen,? Math. Ann.,168, 128?137 (1967). · Zbl 0153.35101 · doi:10.1007/BF01361548
[240] M. Eichler, ?The basis problem for modular forms and the traces of the Hecke operators,? Lect. Notes Math.,320, 75?151 (1973). · Zbl 0258.10013 · doi:10.1007/978-3-540-38509-7_4
[241] M. Eichler, ?Les varietes modulaires de Hilbert et Siegel et les courbes automorphes de Poincare et Shimura,? Asterisque, Nos. 24?25, 99?107 (1975). · Zbl 0303.10030
[242] O. R. Erevik, ?Congruences for the coefficients of3? j(?) and ?j(?)?1728 where j(?) is the modular invariant,? Arb. Univ. Bergen., Mat. Naturvit. Ser., 1966, No. 9, 1?28 (1968).
[243] E. Eschenbach, ?Darstellung von Eisenstein Reihen durch ganze Modulformen niedrigere Dimension,? Abh. Math. Semin. Univ. Hamburg,40, März, 3?16 (1974). · Zbl 0277.10020 · doi:10.1007/BF02993579
[244] N. J. Fine, ?On a system of modular functions connected with the Ramanujan identities,? Tohoku Math. J.,8, No. 2, 149?164 (1956). · Zbl 0073.02904 · doi:10.2748/tmj/1178244978
[245] L. R. Ford, ?A geometric proof of a theorem of Hurwitz,? Proc. Edinburg Math. Soc,35, 59?65 (1917). · JFM 46.1450.03 · doi:10.1017/S0013091500029692
[246] L. R. Ford, ?On the closeness of approach of complex rational fractions to a complex irrational number,? Trans. Am. Math. Soc.,27, 146?154 (1925). · JFM 51.0157.03 · doi:10.1090/S0002-9947-1925-1501304-X
[247] C.-E. Froberg, ?New results on the Kummer conjecture,? BIT (Sver.),14, No. 1, 117?119 (1974). · Zbl 0274.12003 · doi:10.1007/BF01933125
[248] R. J. Fuller, ?Gaussian sums over GL(2,Z/N) and Hecke operators. I, II,? Indiana Univ. Math. J.,24, No. 6, 577?583 (1974);25, No. 1, 69?75 (1976). · doi:10.1512/iumj.1975.24.24042
[249] J. M. Gandhi, ?The nonvanishing of Ramanujan’s?-function,? Am. Math. Mon.,68, No. 8, 757?760 (1961). · Zbl 0218.10061 · doi:10.2307/2311980
[250] J. M. Gandhi, ?Three theorems for the coefficients of the powers of the Dedekind modular form,? Math. Stud.,36, Nos. 1?4, 218?221 (1968). · Zbl 0195.33203
[251] H. Garland, ?Dedekind’s ?-function and the cohomology of infinite dimensional Lie algebras,? Proc. Nat. Acad. Sci. USA,72, No. 7, 2493?2495 (1975). · Zbl 0322.18010 · doi:10.1073/pnas.72.7.2493
[252] H. Garland and J. Lepowski, ?Lie algebra homology and the Macdonald-Kac formulas,? Invent. Math.,34, No. 1, 37?76 (1976). · Zbl 0358.17015 · doi:10.1007/BF01418970
[253] S. Gelbart, ?Automorphic forms on adele groups,? Ann. Math. Stud., No. 83 (1975). · Zbl 0329.10018
[254] S. Gelbart, ?Weil’s representation and the spectrum of the metaplectic group,? Lect. Notes Math.,530 (1976). · Zbl 0365.22017
[255] S. Gelbart and H. Jacquet, ?A relation between automorphic forms on GL(2) and GL(3),? Proc. Nat. Acad. Sci. USA,73, No. 10, 3348?3350 (1976). · Zbl 0373.22008 · doi:10.1073/pnas.73.10.3348
[256] S. Gelbart and P. Sally, ?Intertwining operators and automorphic forms for the metaplectic group,? Proc. Nat. Acad. Sci. USA,72, No. 4, 1406?1410 (1975). · Zbl 0303.22010 · doi:10.1073/pnas.72.4.1406
[257] R. Godement, ?Les travaux de E. Hecke. I, II, III, IV,? Semin. Bourbaki, Secret. Math., 1951?1952, 4-e annee, 2-e ed., Paris, 1959, 51/1?51/7; 59/1?59/8; 1952?1953, 5-e annee, 2-e ed., Paris, 1959, 74/1?74/10; 80/1?80/7.
[258] R. Godement, ?Evaluation d’une somme arithmetique. Remarques,? Bull. Soc. Math. Fr.,101, No. 2, 125?127 (1973). · Zbl 0267.10063 · doi:10.24033/bsmf.1754
[259] L. J. Goldstein, ?A necessary and sufficient condition for the Riemann hypothesis for zeta functions attached to eigenfunctions of the Hecke operators,? Acta Arithm.,15, No. 3, 205?215 (1969). · Zbl 0192.39603
[260] L. J. Goldstein, ?On a conjecture of Hecke concerning elementary class number formulas,? Manuscr. Math.,9, No. 3, 245?305 (1973). · Zbl 0259.12006 · doi:10.1007/BF01303855
[261] L. J. Goldstein, ?Dedekind sums for a Fuchsian group. I, II,? Nagoya Math. J.,50, 21?47 (1973);53, 171?187 (1974). · Zbl 0267.10039 · doi:10.1017/S0027763000015567
[262] L. J. Goldstein, ?On a formula of Hecke,? Isr. J. Math.,17, No. 3, 283?301 (1974). · Zbl 0292.12013 · doi:10.1007/BF02756878
[263] L. J. Goldstein and M. Razar, ?A generalization of Dirichlet’s class number formula,? Duke Math. J.,43, No. 2, 349?358 (1976). · Zbl 0337.10016 · doi:10.1215/S0012-7094-76-04330-1
[264] L. J. Goldstein and M. Razar, ?On the theory of Hecke integrals,? Nagoya Math. J.,63, 93?121 (1976). · Zbl 0346.10011 · doi:10.1017/S002776300001744X
[265] L. J. Goldstein and P. de la Torre, ?On the transformation of log?(?),? Duke Math. J.,41, No. 2, 291?297 (1974). · Zbl 0285.10017 · doi:10.1215/S0012-7094-74-04132-5
[266] L. J. Goldstein and P. de la Torre, ?On a function analogous to log ?(?),? Nagoya Math. J.,59, 169?198 (1975). · Zbl 0335.10031 · doi:10.1017/S0027763000016871
[267] H. Göllnitz, ?Partitionen mit Differenzenbedingungen,? J. Reine Angew. Math.,225, 154?190 (1967).
[268] A. Good, ?Une equation fonctionelle approximative et une moyenne quadratique pour la serie de Dirichlet attachee a la fonction?(n) de Ramanujan,? C. R. Acad. Sci.,277, No. 12, A491-A492 (1973). · Zbl 0264.10019
[269] A. Good, ?Ein Mittelwertsatz für Dirichletreihen die Modulformen assoziiert sind,? Comment. Math. Helv.,49, No. 1, 35?47 (1974). · Zbl 0274.10033 · doi:10.1007/BF02566717
[270] A. Good, ?Approximative Funktionalgleichungen und Mittelwertsätze für Dirichletreihen die Spitzenformen assoziiert sind. Teil I,? Comment. Math. Helv.,50, No. 3, 327?361 (1975). · Zbl 0315.10038 · doi:10.1007/BF02565755
[271] R. C. Grimson, ?Reciprocity theorem for Dedekind sums,? Am. Math. Mon.,81, No. 7, 747?749 (1974). · Zbl 0287.10003 · doi:10.2307/2319565
[272] E. Grosswald, ?Die Werte der Riemannschen Zetafunktion an ungeraden Argumentstellen,? Nachr. Akad. Wiss. Gottingen, II, Math.-Phys. Kl., No. 2 (1970). · Zbl 0206.05902
[273] E. Grosswald, ?Dedekind-Rademacher sums,? Am. Math. Mon.,78, No. 6, 639?644 (1971). · Zbl 0212.07701 · doi:10.2307/2316571
[274] E. Grosswald, ?Dedekind-Rademacher sums and their reciprocity formula,? J. Reine Angew. Math.,251, 161?173 (1971). · Zbl 0223.10012
[275] E. Grosswald, ?Remarks concerning the values of the Riemann zeta function at integral, odd arguments,? J. Number Theory,4, No. 3, 225?235 (1972). · Zbl 0236.10023 · doi:10.1016/0022-314X(72)90049-2
[276] M.-F. Gueho, ?Quaternions et ?k(-1),? Semin. Delange-Pisot-Poitou, Theor. Nombres, Univ. Paris, 1971?1972,13, No. 2, 14/1?14/7 (1973).
[277] K. B. Gundlach, ?Über die Darstellung der ganzen Spitzenformen zu den idealstufen Modulgruppe und die Abschätzung ihrer Fourierkoeffizienten,? Acta Math.,92, 309?345 (1954). · Zbl 0057.03502 · doi:10.1007/BF02392707
[278] K. B. Gundlach, ?Dirichletsche Reihen zur Hilbertschen Modulgruppe,? Math. Ann.,135, No. 4, 294?314 (1958). · Zbl 0133.04301 · doi:10.1007/BF01343245
[279] K. B. Gundlach, ?Die Berechnung von Zetafunktionen mit Vorzeichencharakter an der Stelle 1,? Acta Arithm.,24, No. 2, 201?221 (1973). · Zbl 0363.12012
[280] R. C. Gunning, Lectures on Modular Forms (Ann. Math. Stud., No. 48), Princeton Univ. Press (1962). · Zbl 0178.42901
[281] H. Gupta, ?Partitions. A survey,? J. Res. Nat. Bur. Stand.,B74, No. 1, 1?29 (1970). · Zbl 0203.30701 · doi:10.6028/jres.074B.001
[282] G. H. Hardy, ?A further note on Ramanujan’s arithmetical function?(n),? Proc. Cambr. Phil. Soc, 34, 309?315 (1938). · JFM 64.0099.02 · doi:10.1017/S0305004100020223
[283] G. H. Hardy, Ramanujan ?Twelve Lectures on Subjects Suggested by His Life and Work, Cambr. Univ. Press, Cambridge (1940); Macmillan, New York (1940); reprint, Chelsea, New York (1959). · JFM 67.0002.09
[284] E. Hecke, Mathematische Werke, Vandenhoeck und Ruprecht, Göttingen (1959).
[285] K. Heegner, ?Diophantische Analysis und Modulfunktionen,? Math. Z.,56, 227?253 (1952). · Zbl 0049.16202 · doi:10.1007/BF01174749
[286] D. Hejhal, ?The Selberg trace formula and the Riemann zeta function,? Duke Math. J.,43, No. 3, 441?482 (1976). · Zbl 0346.10010 · doi:10.1215/S0012-7094-76-04338-6
[287] G. Herglotz, ?Über die Kroneckersche Grenzformel für reelle quadratische Körper. I, II,? Ber. Verh. Saechs. Akad. Wiss. Leipzig,75, 3?14, 31?37 (1923). · JFM 49.0125.03
[288] O. Herrmann, ?Über Hilbertsche Modulfunktionen und die Dirichletschen Reihen mit Eulerscher Produktentwicklung,? Math. Ann.,127, No. 4, 357?400 (1954). · Zbl 0055.31202 · doi:10.1007/BF01361131
[289] O. Herrmann, ?Kongruenzeigenschaften der Partitionenfunktion,? J. Number Theory,1, No. 4, 431?458 (1969). · Zbl 0185.15501 · doi:10.1016/0022-314X(69)90005-5
[290] O. Herrman, ?Über die Berechnung der Fourierkoeffizienten der Funktion j(?),? J. Reine Angew. Math.,274?275, 187?195 (1975).
[291] Hijikata Hiroaki, ?On certain identities between the traces of Hecke operators,? Proc. Jpn. Acad.,48, No. 8, 585?588 (1972). · Zbl 0255.10028 · doi:10.3792/pja/1195519567
[292] Hijikata Hiroaki, ?Explicit formula of the traces of Hecke operators for ?0(N),? J. Math. Soc. Jpn.,26, No. 1, 56?82 (1974). · Zbl 0266.12009 · doi:10.2969/jmsj/02610056
[293] Hijikata Hiroaki and Saito Hiroshi, ?On the representability of modular forms by theta series,? in: Number Theory, Algebraic Geometry and Commutative Algebra?in honor of Yasui Akiziki, Tokyo, Japan (1973), pp. 13?22.
[294] Hiramatsu Toyokazu, ?Modular forms obtained from L-functions with Grössen-characters of Q(??3),? Comment. Math. Univ. St. Pauli,14, No. 2, 65?70 (1966).
[295] Hiramatsu Toyokazu, ?Eichler maps and hyperbolic Fourier expansion,? Nagoya Math. J.,40, 173?192 (1970). · Zbl 0223.10011 · doi:10.1017/S0027763000013945
[296] F. Hirzebruch, ?Free involutions on manifolds and some elementary number theory,? in: Sympos. Mat. Ist. Naz. Alta Mat., 1969?1970, Vol. 5, London-New York (1971), pp. 411?419.
[297] F. Hirzebruch, ?The signature theorem: Reminiscences and recreation,? Ann. Math. Stud., No. 70, 3?31 (1971). · Zbl 0252.58009
[298] F. Hirzebruch, ?Hilbert modular surfaces,? Enseign. Math.,19, Nos. 3?4, 183?281 (1973). · Zbl 0285.14007
[299] F. Hirzebruch, ?Kurven der Hilbertschen Modulflächen und Klassenzahlrelationen,? Lect. Notes Math.,412, 75?93 (1974). · Zbl 0301.14010 · doi:10.1007/BFb0066155
[300] F. Hirzebruch, ?Hubert modular surfaces and class numbers,? Asterisque, Nos. 32?33, 151?164 (1976).
[301] F. Hirzebruch and D. Zagier, ?Intersection numbers of curves on Hilbert modular surfaces and modular forms of nebentypus,? Invent. Math.,36, 57?113 (1976). · Zbl 0332.14009 · doi:10.1007/BF01390005
[302] T. Hjelle and T. Kløve, ?Congruence properties and density problems for the Fourier coefficients of modular forms,? Math. Scand.,23, No. 1, 160?166 (1968). · Zbl 0184.07401 · doi:10.7146/math.scand.a-10905
[303] M. J. Hodel, ?A note on inversions and generalized Dedekind sums,? Abh. Math. Semin. Univ. Hamburg,43, 146?157 (1975). · Zbl 0304.10005 · doi:10.1007/BF02995944
[304] Honda Taira, Miyawaki Isao, ?Zeta functions of elliptic curves of 2-power conductor,? J. Math. Soc. Jpn.,26, No. 2, 362?373 (1974). · Zbl 0273.14007 · doi:10.2969/jmsj/02620362
[305] Igusa Jun-Ichi, ?Kroneckerian model of fields of elliptic modular functions,? Am. J. Math.,81, No. 3, 561?577 (1959). · Zbl 0093.04502 · doi:10.2307/2372914
[306] Ihara Yasutaka, ?On certain arithmetical Dirichlet series,? J. Math. Soc. Jpn.,16, No. 3, 215?225 (1964). · Zbl 0126.07101
[307] Ihara Yasutaka, ?Hecke polynomials as congruence ? functions in elliptic modular case,? Ann. Math.,85, No. 2, 267?295 (1967). · Zbl 0181.36501 · doi:10.2307/1970442
[308] Iseki Sho, ?The transformation formula for the Dedekind modular function and related functional equations,? Duke Math. J.,24, No. 4, 653?662 (1957). · Zbl 0093.25903 · doi:10.1215/S0012-7094-57-02473-0
[309] Iseki Sho, ?A paritition function with some congruence condition,? Am. J. Math.,81, No. 4, 939?961 (1959). · Zbl 0094.25605 · doi:10.2307/2372997
[310] Iseki Sho, ?A generalization of a functional equation related to the theory of partitions,? Duke Math. J.,27, No. 1, 95?110 (1960). · Zbl 0095.03102 · doi:10.1215/S0012-7094-60-02710-1
[311] Iseki Sho, ?A proof of a functional equation related to the theory of partitions,? Proc. Am. Math. Soc.,12, No. 3, 502?505 (1961).
[312] Ishikawa Hirofumi, ?On the trace formula for Hecke operators,? J. Fac. Sci. Univ. Tokyo, Sec 1A,20, No. 2, 217?238 (1973). · Zbl 0267.10037
[313] Ishikawa Hirofumi, ?On trace of Hecke operators for discontinuous groups operating on the product of the upper half planes,? J. Fac. Sci. Univ. Tokyo, Sec 1A,21, No. 3, 357?376 (1974). · Zbl 0295.10023
[314] Iwasaki Koziro, ?Note on the modular forms,? Proc. Jpn. Acad.,39, No. 6, 333?337 (1963). · Zbl 0131.31002 · doi:10.3792/pja/1195523027
[315] H. Jacquet, Automorphic Forms on GL(2). Part II, Lect. Notes Math.,278 (1972). · Zbl 0243.12005
[316] H. Jacquet and R. P. Langlands, Automorphic Forms on GL(2), Lect. Notes Math.,114 (1970). · Zbl 0236.12010
[317] H. Jacquet, I. Pyatetskii-Shapiro, and J. Shalika, Construction of Cusp Forms on GL(3), Lect. Note #16, Department of Mathematics, Univ. of Maryland (1975).
[318] H. Jacquet, I. Pyatetskii-Shapiro, and J. Shalika, ?Construction de formes automorphes pourle groupe GL(3),? C. R. Acad. Sci.,282, No. 2, A91-A93 (1976).
[319] H. Jacquet and J. Shalika, ?Hecke theory for GL(3),? Compos. Math.,29, No. 1, 75?87 (1974). · Zbl 0318.22022
[320] H. Joris, ?Un ?-theoreme pour la fonction arithmetique de Ramanujan,? C. R. Acad. Sci.,272, No. 4, A295 (1971).
[321] H. Joris, ??-Sätze für zwei arithmetische Funktionen,? Comment. Math. Helv.,47, No. 2, 220?248 (1972). · Zbl 0248.12009 · doi:10.1007/BF02566800
[322] H. Joris, ??-Sätze für gewisse multiplikative arithmetische Funktionen,? Comment. Math. Helv.,48, No. 4, 409?435 (1973). · Zbl 0282.12009 · doi:10.1007/BF02566133
[323] H. Joris, ?An ?-result for coefficients of cusp forms,? Mathematika (Gr. Britain),22, No. 1, 12?19 (1975). · Zbl 0342.10015 · doi:10.1112/S0025579300004447
[324] H. Kappus, ?Darstellungen von Korrespondenzen algebraischer Funktionenkörper und ihre Spuren,? J. Reine Angew. Math.,210, Nos. 3?4, 123?140 (1962). · Zbl 0109.26802
[325] H. Kappus, ?Eine Spurformel für inseparable Korrespondenzen algebraischer Funktionenkörper,? Arch. Math.,18, No. 4, 378?382 (1967). · Zbl 0155.49401 · doi:10.1007/BF01898829
[326] Katayama Koji, ?Kronecker’s limit formulas and their applications,? J. Fac. Sci. Univ. Tokyo,13, No.1, 1?44 (1966). · Zbl 0148.27804
[327] Katayama Koji, ?On certain zeta functions attached to the tensor representations of SL(2,R),? Am. J. Math.,92, No. 4, 869?893 (1970). · Zbl 0212.06703 · doi:10.2307/2373399
[328] Katayama Koji, ?On zeta-theta functions,? J. Math. Soc. Jpn.,24, No. 2, 307?332 (1972). · Zbl 0239.10024 · doi:10.2969/jmsj/02420307
[329] Katayama Koji, ?A supplement to my paper ’On zeta-theta functions,? J. Math. Soc. Jpn.,25, No. 3, 545?546 (1973). · Zbl 0252.10044 · doi:10.2969/jmsj/02530545
[330] Katayama Koji, ?On Ramanujan’s formula for values of Riemann zeta function at positive odd integers,? Acta Arithm.,22, No. 2, 149?155 (1973). · Zbl 0222.10040
[331] Katayama Koji, ?Zeta functions, Lambert series, and arithmetic functions analogous to Ramanujan’s?-function. I, II,? J. Reine Angew. Math.,268?269, 251?270 (1974);282, 11?34 (1976). · Zbl 0289.10017
[332] Katayama Koji, ?On the values of ray-class L-functions for real quadratic fields,? J. Math. Soc. Jpn.,28, No. 3, 455?482 (1976). · Zbl 0328.12004 · doi:10.2969/jmsj/02830455
[333] N. M. Katz, ?p-Adic properties of modular schemes and modular forms,? Lect. Notes Math.,350, 69?190 (1973). · Zbl 0271.10033 · doi:10.1007/978-3-540-37802-0_3
[334] N. M. Katz, ?Higher congruences between modular forms,? Ann. Math.,101, No. 2, 332?367 (1975). · Zbl 0356.10020 · doi:10.2307/1970994
[335] H. Keller, ?Une identite generale de l’arithmetique,? C. R. Acad. Sci.,280, No. 24, A1659-A1660 (1975). · Zbl 0308.10027
[336] M. A. Kenku, ?Determination of the even discriminants of complex quadratic fields of class-number 2,? Proc. London Math. Soc.,22, No. 4, 734?746 (1971). · Zbl 0215.07203 · doi:10.1112/plms/s3-22.4.734
[337] M. A. Kenku, ?On the L-function of quadratic forms,? J. Reine Angew. Math.,276, 36?43 (1975).
[338] Kitaoka Yoshiyuki, ?Representations of quadratic forms and their application to Selberg’s zeta functions,? Nagoya Math. J.,63, 153?162 (1976). · Zbl 0334.10010 · doi:10.1017/S0027763000017475
[339] Kitaoka Yoshiyuki, ?On a space of some theta functions,? Nagoya Math. J.,42, 89?93 (1971). · Zbl 0221.10031 · doi:10.1017/S0027763000014264
[340] Kitaoka Yoshiyuki, ?A note on Hecke operators and theta series,? Nagoya Math. J.,42, 189?195 (1971). · Zbl 0221.10031 · doi:10.1017/S002776300001432X
[341] Kitaoka Yoshiyuki, ?On the relation between the positive definite quadratic forms with the same representation numbers,? Proc. Jpn. Acad.,47, No. 5, 439?441 (1971). · Zbl 0225.10029 · doi:10.3792/pja/1195519924
[342] Kitaoka Yoshiyuki, ?A simple proof on the functional equation of a certain L-function,? J. Number Theory,3, No. 2, 155?158 (1971). · Zbl 0229.10022 · doi:10.1016/0022-314X(71)90032-1
[343] Kitaoka Yoshiyuki, ?Quaternary even positive definite quadratic forms of prime discriminant,? Nagoya Math. J.,52, 147?161 (1973). · Zbl 0294.10014 · doi:10.1017/S0027763000015944
[344] Kitaoka Yoshiyuki, ?Class numbers of positive definite quinary quadratic forms,? Jpn. J. Math. (N.S.),1, No. 1, 85?100 (1975). · Zbl 0317.10033
[345] H. Klingen, ?Über die Werte der Dedekindschen Zetafunktion,? Math. Ann.,145, No. 3, 265?272 (1962). · Zbl 0101.03002 · doi:10.1007/BF01451369
[346] H. Klingen, ?Über den arithmetischen Charakter der Fourierkoeffizienten von Modulformen,? Math. Ann.,147, No. 2, 176?188 (1962). · Zbl 0104.26502 · doi:10.1007/BF01470949
[347] H. D. Kloosterman, ?Das Verhalten der Dedekindschen Funktion ?(?) unter Modulsubstitutionen,? Math. Ann.,150, No. 2, 130?135 (1963). · Zbl 0118.07901 · doi:10.1007/BF01470839
[348] T. Kløve, ?Recurrence formulae for the coefficients of modular forms and congruences for the partition function and for the coefficients of j(?), (j(?)?1728)/2, and (j(?))?? Math. Scand.,23, No. 1 (1968). · Zbl 0184.07302
[349] T. Kløve, ?On a class of partition congruences,? Arb. Univ. Bergen. Mat.-Naturvit. Ser., No. 11, 1?10 (1969).
[350] T. Kløve, ?Recurrence formulae for the coefficients of modular forms,? Math. Scand.,26, No. 1, 221?232 (1970). · Zbl 0203.39202 · doi:10.7146/math.scand.a-10978
[351] T. Kløve, ?Density problems for p(n),? J. London Math. Soc.,2, No. 3, 504?508 (1970). · Zbl 0199.36702 · doi:10.1112/jlms/2.Part_3.504
[352] M. Kneser, ?Lineare Relationen zwischen Darstellungsanzahlen quadratischer Formen,? Math. Ann.,168, 31?39 (1967). · Zbl 0146.05901 · doi:10.1007/BF01361543
[353] M. I. Knopp, Modular Functions in Analytic Number Theory, Markham, Chicago (1970). · Zbl 0259.10001
[354] M. I. Knopp, ?Remarks on a problem of Rademacher in the theory of modular forms,? J. Res. Nat. Bur. Stand., B77, Nos. 3?4, 81?83 (1973). · Zbl 0274.10030 · doi:10.6028/jres.077B.008
[355] M. I. Knopp and J. R. Smart, ?On Kloosterman sums connected with modular forms of half-integral dimension,? Ill. J. Math.,8, No. 3, 480?487 (1964). · Zbl 0124.28002
[356] M. I. Knopp and J. R. Smart, ?Hecke basis theorems for groups of genus 0,? J. Res. Nat. Bur. Stand.,B74, No. 3, 131?148 (1970). · Zbl 0205.09601 · doi:10.6028/jres.074B.013
[357] M. Koecher, ?Ein neuer Beweis der Kroneckerschen Grenzformel,? Arch. Math.,4, No. 4, 316?321 (1953). · Zbl 0051.31802 · doi:10.1007/BF01899895
[358] Koike Masao, ?Congruences between modular forms and functions and applications to the conjecture of Atkin,? J. Fac. Sci. Univ. Tokyo, Sec. 1A,20, No. 1, 129?169 (1973). · Zbl 0256.10016
[359] Koike Masao, ?On some p-adic properties of the Eichler-Selberg trace formula,? Nagoya Math. J.,56, 45?52 (1975). · Zbl 0301.10026 · doi:10.1017/S0027763000016366
[360] O. Kolberg, ?Some identities involving the partition function,? Math. Scand.,5, No. 1, 77?92 (1957). · Zbl 0080.03303 · doi:10.7146/math.scand.a-10492
[361] O. Kolberg, ?Some congruences modulo 13 involving the partition function,? Arb. Univ. Bergen. Mat.-Naturvit. Ser., No. 9, 1?11 (1960).
[362] O. Kolberg, ?Some remarks on a class of partition congruences,? Arb. Univ. Bergen. Mat.-Naturvit. Ser., No. 18, 1?8 (1961).
[363] O. Kolberg, ?Congruences for the coefficients of the modular invariant j(?) modulo powers of 2,? Arb. Univ. Bergen. Mat.-Naturvit. Ser., No. 16, 1?9 (1961).
[364] O. Kolberg, ?The coefficients of j(?) modulo powers of 3,? Arb. Univ. Bergen. Mat.-Naturvit. Ser., No. 16, 1?7 (1962). · Zbl 0168.29502
[365] O. Kolberg, ?Congruences for the coefficients of the modular invariant j(?),? Math. Scand.,10, No. 2, 173?181 (1962). · Zbl 0109.03003 · doi:10.7146/math.scand.a-10525
[366] O. Kolberg, ?Note on Ramanujan’s function?(n),? Math. Scand.,10, No. 2, 171?172 (1962). · Zbl 0109.03101 · doi:10.7146/math.scand.a-10524
[367] O. Kolberg, ?Congruences for Ramanujan’s function?(n),? Arb. Univ. Bergen, Math.-Naturvit. Ser., No. 11, 1?8 (1962). · Zbl 0109.03101
[368] O. Kolberg, ?Note on the Eisenstein series of ?0(p),? Arb. Univ. Bergen, Math.-Naturvit. Ser., No. 6, 1?20 (1968). · Zbl 0233.10013
[369] O. Kolberg, ?On the Fourier coefficients of the modular invariant j(?),? Arb. Univ. Bergen, Mat.-Naturvit. Ser., No. 3, 1?8 (1969). · Zbl 0238.12008
[370] Konno Shuji, ?On Kronecker’s limit formula in a totally imaginary quadratic field over a totally real algebraic number field,? J. Math. Soc. Jpn.,17, No. 4, 411?424 (1965). · Zbl 0147.03603 · doi:10.2969/jmsj/01740411
[371] B. Kostant, ?On Macdonald’s ?-function formula, the Laplacian, and generalized exponents,? Adv. Math.,20, No. 2, 179?212 (1976). · Zbl 0339.10019 · doi:10.1016/0001-8708(76)90186-9
[372] E. Krätzel, ?Über die Anzahl der Darstellungen von natürlichen Zahlen als Summe von 4k + 2 Quadraten,? Wiss. Z. Friedrich-Schiller-Univ., Jena, Math.-Naturwiss. R.,11, Nos. 1?2, 115?120 (1962).
[373] E. Krätzel, ?Höhere Thetafunktionen. I, II,? Math. Nachr.,30, Nos. 1?2, 17?32, 33?46 (1965). · Zbl 0142.34002 · doi:10.1002/mana.19650300103
[374] E. Krätzel, ?Kubische und biquadratische Gausssche Summen,? J. Reine Angew. Math.,228, 159?165 (1967).
[375] E. Krätzel, ?Zur Frage der Produktentwicklung höherer Thetafunktionen,? Math. Nachr.,71, 291?302 (1976). · Zbl 0292.33011 · doi:10.1002/mana.19760710125
[376] Kubota Tomio, ?Anwendung Jacobischer Thetafunktionen auf die Potenzreste,? Nagoya Math. J.,19, 1?13 (1961). · Zbl 0104.03801 · doi:10.1017/S002776300000235X
[377] Kubota Tomio, ?Über quadratische Charaktersummen,? Nagoya Math. J.,19, 15?25 (1961). · Zbl 0107.03601 · doi:10.1017/S0027763000002361
[378] Kubota Tomio, ?Reciprocities in Gauss’ and Eisenstein’s number fields,? J. Reine Angew. Math.,208, Nos. 1?2, 35?50 (1961). · Zbl 0202.33302
[379] Kubota Tomio, ?Über eine Verallgemeinerung der Reziprozität der Gaussschen Summen,? Math. Z.,82, No. 2, 91?100 (1963). · Zbl 0201.37503 · doi:10.1007/BF01111796
[380] Kubota Tomio, ?Some arithmetical applications of an elliptic function,? J. Reine Angew. Math.,214-215, 141?145 (1964). · Zbl 0146.27901
[381] Kubota Tomio, ?Ein arithmetischer Satz über eine Matrizengruppe,? J. Reine Angew. Math.,222, Nos. 1?2, 55?57 (1966).
[382] Kubota Tomio, ?An application of the power residue theory to some Abelian functions,? Nagoya Math, J.,27, No. 1, 51?54 (1966). · Zbl 0168.29601 · doi:10.1017/S0027763000011843
[383] Kubota Tomio, ?On a special kind of Dirichlet series,? J. Math. Soc. Jpn.,20, Nos. 1?2, 193?207(1968). · Zbl 0157.10202 · doi:10.2969/jmsj/02010193
[384] Kubota Tomio, ?Über diskontinuierliche Gruppen Picardschen Typus und zugehörige Eisensteinsche Reihen,? Nagoya Math. J.,32, 259?271 (1968). · Zbl 0159.31303 · doi:10.1017/S0027763000026684
[385] Kubota Tomio, ?On automorphic functions and the reciprocity law in a number field,? Lectures in Mathematics, Department of Mathematics, Kyoto Univ., No. 2, Tokyo (1969). · Zbl 0231.10017
[386] Kubota Tomio, ?On a classical theta function,? Nagoya Math. J.,37, 183?189 (1970). · Zbl 0192.39602 · doi:10.1017/S0027763000013386
[387] Kubota Tomio, ?Some results concerning reciprocity and functional analysis,? in: Actes Congr. Int. Mathematiciens, 1970, Vol. 1, Paris (1971), pp. 395?399.
[388] Kubota Tomio, ?Some results concerning reciprocity law and real analytic automorphic functions,? in: Proc. Sympos. Pure Math., Vol. 20, Number Theory, Providence, R. I. (1971), pp. 382?395. · Zbl 0215.36103 · doi:10.1090/pspum/020/0340221
[389] Kubota Tomio, ?Some number-theoretic results on real analytic automorphic forms,? Lect. Notes Math.,185, 87?96 (1971). · Zbl 0215.36103 · doi:10.1007/BFb0058766
[390] Kubota Tomio, Elementary Theory of Eisenstein Series, Kodansha, Tokyo, Wiley, New York (1973).
[391] Kuga Michio, ?On a uniformity of distribution ofo-cycles and the eigenvalues of Hecke’s operators. I, II,? Sci. Papers Coll. Gen. Educ. Univ. Tokyo,10, No. 1, 1?16 (1960); No. 2, 171?186 (1960). · Zbl 0093.08101
[392] Kuga Michio and Shimura Goro, ?On the zeta function of a fibre variety whose fibres are Abelian varieties,? Ann. Math.,82, No. 3, 478?539 (1965). · Zbl 0166.16801 · doi:10.2307/1970709
[393] D. B. Lahiri, ?Some arithmetical properties of the Fourier coefficients of the modular invariant j(?),? Current. Sci.,34, No. 7, 208 (1965).
[394] D. B. Lahiri, ?Congruences for the coefficients of the modular invariant j(?),? Sci. Cult.,31, No. 12, 629?630 (1965).
[395] D. B. Lahiri, ?Congruences for the Fourier coefficients of the modular invariant j(?),?, Proc. Nat. Inst. Sci. India,A32, No. 1, 95?103 (1966). · Zbl 0148.27306
[396] D. B. Lahiri, ?Identities connecting the partition, divisor, and Ramanujan’s functions,? Proc. Nat. Inst. Sci. India,A34, Suppl. No. 1, 96?103 (1968). · Zbl 0215.06902
[397] D. B. Lahiri, ?Some arithmetical identities for Ramanujan’s and divisor functions,? Bull. Austral. Math. Soc.,1, No. 3, 307?314 (1969). · Zbl 0176.32403 · doi:10.1017/S0004972700042179
[398] H. Lang, ?Eisensteinsche Reihen höherer Stufe im Falle dem komplexen Multiplikation,? Abh. Math. Semin. Univ. Hamburg,35, Nos. 3?4, 242?250 (1971). · Zbl 0213.05603 · doi:10.1007/BF02993628
[399] H. Lang, ?Über Anwendungen höherer Dedekindscher Summen auf die Struktur elementar-arithmetischer Klasseninvarianten reell-quadratischer Zahlkörper,? J. Reine Angew. Math.,254, 17?32 (1972). · Zbl 0244.12012
[400] H. Lang, ?Über Bernoullische Zahlen in reell-quadratischen Zahlkörpern,? Acta Arithm.,22, No. 4, 423?437 (1973). · Zbl 0231.12004
[401] H. Lang, ?Eine Invariante modulo 8 von Geschlechtern in reell-quadratischen Zahlkörpern,? Math. Ann.,217, No. 3, 263?265 (1975). · Zbl 0297.12005 · doi:10.1007/BF01436178
[402] H. Lang, ?Über einfache periodische Kettenbruche und Vermutungen von P. Chowla und S. Chowla,? Acta Arithm.,28, No. 4, 419?428 (1976). · Zbl 0278.10032
[403] H. Lang and R. Schertz, ?Kongruenzen zwischen Klassenzahlen quadratischer Zahlkörper,? J. Number Theory,8, No. 3, 352?365 (1976). · Zbl 0335.12008 · doi:10.1016/0022-314X(76)90014-7
[404] S. Lang, Introduction to Modular Forms, Springer, Berlin (1976). · Zbl 0344.10011
[405] R. P. Langlands, ?Euler products,? Matematika,15, No. 1, 14?43 (1971).
[406] R. P. Langlands, ?Problems in the theory of automorphic forms,? Lect. Notes Math.,l70, 18?61 (1970). · Zbl 0225.14022 · doi:10.1007/BFb0079065
[407] D. H. Lehmer, ?Properties of the coefficients of the modular invariant j(?),? Am. J. Math.,64, 488?502 (1942). · Zbl 0063.03473 · doi:10.2307/2371699
[408] D. H. Lehmer, ?The primality of Ramanujan’s tau function,? Am. Math. Month.,72, No. 2, Part 2, 15?18 (1965). · Zbl 0151.02602 · doi:10.2307/2313305
[409] D. H. Lehmer, ?Note on the distribution of Ramanujan’s? function,? Math. Comput.,24, No. 111, 741?743 (1970).
[410] E. Lehmer, ?On the location of Gauss sums,? Math. Tables Other Aids Comput.,10, No. 56, 194?202 (1956). · Zbl 0073.03001 · doi:10.2307/2001914
[411] J. Lehner, ?Ramanujan identities involving the paritition function for the moduli 11?,? Am. J. Math.,65, 492?520 (1943). · Zbl 0060.10007 · doi:10.2307/2371972
[412] J. Lehner, ?Divisibility properties of the Fourier coefficients of the modular invariant j(?),? Am. J. Math.,71, 136?148 (1949). · Zbl 0031.39502 · doi:10.2307/2372101
[413] J. Lehner, ?Further congruence properties of the Fourier coefficients of the modular invariant j(?),? Am. J. Math.,71, 373?386 (1949). · Zbl 0032.15902 · doi:10.2307/2372252
[414] J. Lehner, ?Proof of Ramanujan’s partition congruence for the modulus 113,? Proc. Am. Math. Soc.,1, 172?181 (1950). · Zbl 0037.31303
[415] J. Lehner, ?The Fourier coefficients of automorphic forms belonging to a class of horocyclic groups,? Mich. Math. J.,4, No. 3, 265?279 (1957). · Zbl 0081.07602 · doi:10.1307/mmj/1028997959
[416] J. Lehner, ?Magnitude of the Fourier coefficients of automorphic forms of negative dimension,? Bull. Am. Math. Soc.,67, No. 6, 603?606 (1961). · Zbl 0106.28702 · doi:10.1090/S0002-9904-1961-10707-6
[417] J. Lehner, Discontinuous Groups and Automorphic Functions, Am. Math. Soc., Providence, R.I. (1964). · Zbl 0178.42902
[418] J. Lehner, ?On the multipliers of the Dedekind modular function,? J. Res. Nat. Bur. Stand.,B72, No. 4, 253?261 (1968). · Zbl 0207.38102 · doi:10.6028/jres.072B.025
[419] J. Lehner, Lectures on Modular Forms, Nat. Bureau Standards, Washington (1969). · Zbl 0189.36801
[420] J. Lehner, ?Automorphic integrals with preassigned periods,? J. Res. Nat. Bur. Stand.,B73, No. 2, 153?161 (1969). · Zbl 0185.33501 · doi:10.6028/jres.073B.016
[421] A. Leutbecher, ?Über Automorphiefaktoren und die Dedekindschen Summen,? Glasgow Math. J.,11, No. 1, 41?57 (1970). · Zbl 0214.30001 · doi:10.1017/S0017089500000823
[422] J. Lewittes, ?Analytic continuation of the series ?(m + nz)?S,? Trans. Am. Math. Soc.,159, 505?509 (1971). · Zbl 0226.30005
[423] J. Lewittes, ?Analytic continuation of Eisenstein series,? Trans. Am. Math. Soc.,171, 469?490 (1972). · Zbl 0253.10022 · doi:10.1090/S0002-9947-1972-0306148-1
[424] G. Ligozat, ?Courbes modulaires de genre 1,? Bull. Soc. Math. Fr., Mem. No. 43 (1975). · Zbl 0322.14011
[425] Ju. V. Linnik, ?Additive problems and eigenvalues of the modular operators,? in: Proc. Int. Congr. Math. Aug. 1962, Djursholm, Uppsala (1963), pp. 270?284.
[426] J. H. van Lint, Hecke Operators and Euler Products, Drukkerij Luctor et Emergo, Leiden (1957). · Zbl 0077.08202
[427] J. H. van Lint, ?On the multiplier system of Riemann-Dedekind function,? Proc. K. Ned. Akad. Wet., Ser. A,61, No. 5, 522?527 (1958); Indag. Math.,20, No. 5, 522?527 (1958). · Zbl 0085.30001
[428] J. H. van Lint, ?Linear relations for certain modular forms,? Math. Nachr.,20, Nos. 1?2, 123?126 (1959). · Zbl 0092.07601 · doi:10.1002/mana.19590200111
[429] Li Wen-Ch’ing W., ?New forms and functional equations,? Math. Ann.,212, No. 4, 285?315 (1975). · Zbl 0278.10026 · doi:10.1007/BF01344466
[430] G. Lomadze, ?Über die Darstellung der Zahlen durch einige quaternäre quadratische Formen,? Acta Arithm.,5, No. 2, 125?170 (1959).
[431] G. Lomadze, ?Über die Darstellung der Zahlen durch einige ternäre quadratische Formen,? Acta Arithm.,6, No. 3, 225?275 (1961).
[432] J. H. Loxton, ?Products related to Gauss sums,? J. Reine Angew. Math.,268?69, 53?57 (1974). · Zbl 0293.10019
[433] H. Maass, ?Über eine neue Art von nichtanalytischen automorphen Funktionen und die Bestimmung Dirichletseher Reihen durch Funktionalgleichungen,? Math. Ann.,121, 141?183 (1949). · doi:10.1007/BF01329622
[434] H. Maass, ?Über die Verteilung der zweidimensionalen Untergitter in einem euklidischen Gitter,? Math. Ann.,137, No. 4, 319?327 (1959). · Zbl 0085.06902 · doi:10.1007/BF01360968
[435] H. Maass, ?Über die räumliche Verteilung der Punkte in Gittern mit indefiniter Metrik,? Math. Ann.,138, No. 4, 287?315 (1959). · Zbl 0089.06102 · doi:10.1007/BF01344150
[436] I. G. Macdonald, ?Affine root systems and Dedekind’s ?-function,? Invent. Math.,15, No. 2, 91?143 (1972). · Zbl 0244.17005 · doi:10.1007/BF01418931
[437] K. Mahler, ?An arithmetic property of groups of linear transformations,? Acta Arithm.,15, No. 2, 197?203 (1959). · Zbl 0089.26803
[438] K. Mahler, ?On the coefficients of the 2n-th transformation polynomial for j(?),? Acta Arithm.,21, 89?97 (1972). · Zbl 0257.10013
[439] K. Mahler, ?On the coefficients of transformation polynomials for the modular function,? Bull. Austral. Math. Soc.,10, No. 2, 197?218 (1974). · Zbl 0269.10013 · doi:10.1017/S0004972700040831
[440] Yu. I. Manin, ?Explicit formulas for the eigenvalues of Hecke operators,? Acta Arithm.,24, No. 3, 239?249 (1973). · Zbl 0273.10018
[441] F. Mautner, ?Spherical functions and Hecke operators,? in: Lie Groups and Their Representations, Budapest (1975), pp. 555?576.
[442] P. J. McCarthy, ?A congruence property of Ramanujan’s function,? Q. J. Math.,8, No. 30, 141?142 (1957). · Zbl 0077.26103 · doi:10.1093/qmath/8.1.141
[443] P. J. McCarthy, ?Some congruences involving Ramanujan’s function?(n),? Math. Student,27, Nos. 1?2, 13?15 (1959).
[444] A. D. McGettrick, ?On the biquadratic Gauss sum,? Proc. Cambr. Phil. Soc.,71, No. 1, 79?83 (1972). · Zbl 0226.10042 · doi:10.1017/S0305004100050301
[445] A. D. McGettrick, ?A result in the theory of Weierstrass elliptic functions,? Proc. London Math. Soc.,25, No. 1, 41?54 (1972). · Zbl 0251.10027 · doi:10.1112/plms/s3-25.1.41
[446] G. Meinardus, ?Über die Kroneckersche Grenzformel,? Math. Z.,62, No. 4, 347?351 (1955). · Zbl 0065.31601 · doi:10.1007/BF01180642
[447] H. Menzer, ?Transformation spezieller Dirichletscher Reihen. I, II,? Math. Nachr.,73, 297?303,305-313 (1976). · Zbl 0289.10029 · doi:10.1002/mana.19760730122
[448] C. Meyer, Die Berechnung der Klassenzahl Abelscher Körper über quadratischen Zahlkörpern, Akad.-Verlag, Berlin (1957). · Zbl 0079.06001
[449] C. Meyer, ?Über einige Anwendungen Dedekindscher Summen,? J. Reine Angew. Math.,198, Nos. 3?4, 143?203 (1957). · Zbl 0079.10303
[450] C. Meyer, ?Bemerkungen zu den allgemeinen Dedekindschen Summen,? J. Reine Angew. Math.,205, Nos. 3?4, 186?196 (1961). · Zbl 0097.26401
[451] C. Meyer, ?Über die Bildung von Klasseninvarianten binärer quadratischer Formen mittels Dedekindscher Summen,? Abh. Math. Semin. Univ. Hamburg,27, Nos. 3?4, 206?230 (1964). · Zbl 0122.05201 · doi:10.1007/BF02993218
[452] C. Meyer, ?Bemerkungen zum Satz von Heegner-Stark über die imaginär-quadratischen Zahlkörper mit der Klassenzahl Eins,? J. Reine Angew. Math.,242, 179?214 (1970). · Zbl 0218.12007
[453] M. Mikolas, ?Über gewisse Lambertsche Reihen, I: Verallgemeinerung der Modulfunktion ?(?) und ihrer Dedekindschen Transformationsformel,? Math. Z.,68, No. 1, 100?110 (1957). · Zbl 0078.07003 · doi:10.1007/BF01160334
[454] M. Mikolas, ?On certain sums generating the Dedekind sums and their reciprocity laws,? Pac. J. Math.,7, No. 2, 1167?1178 (1957). · Zbl 0081.04302 · doi:10.2140/pjm.1957.7.1167
[455] Miyake Toshitsune, ?Decomposition of Jacobian varieties and Dirichlet series of Hecke type,? Am. J. Math.,92, No. 3, 671?707 (1970). · Zbl 0204.54202 · doi:10.2307/2373368
[456] Miyake Toshitsune, ?On automorphic forms on GL2 and Hecke operators,? Ann. Math.,94, No. 1, 174?189 (1971). · Zbl 0319.10035 · doi:10.2307/1970741
[457] Modular Functions of One Variable. I, II, III, IV. Proc. Int. Summer School, Univ. Antwerp., RUCA, July 17?Aug. 3, 1972. W. Kuyk, Ed., Lect. Notes Math.,320 (1973); P. Deligne and W. Kuyk, Eds., Lect. Notes Math.,349 (1973); W. Kuyk and J. P. Serre, Eds., Lect. Notes Math.,350 (1973); B. J. Birch and W. Kuyk, Eds., Lect. Notes Math.,476 (1975).
[458] R. V. Moody, ?Macdonald identities and Euclidean Lie algebras,? Proc. Am. Math. Soc.,48, No. 1, 43?52 (1975). · Zbl 0315.17003 · doi:10.1090/S0002-9939-1975-0442048-2
[459] L. J. Mordell, ?On Mr. Ramanujan’s empirical expansions of modular functions,? Proc. Cambr. Phil. Soc.,19, 117?124 (1919).
[460] L. J. Mordell, ?On some series whose nth term involves the number of classes of binary quadratics of determinant-n,? Messenger of Math.,49, No. 5, 65?72 (1919).
[461] L. J. Mordell, ?On the generating function of the series F(n)qn, where F(n) is the number of uneven classes of binary quadratics of determinant-n,? Messenger Math.,50, No. 8, 113?128 (1920).
[462] L. J. Mordell, ?The definite integral \(\int\limits_{ - \infty }^\infty {\frac{{e^{ax^2 + bx} }}{{e^{cx} + dx}} } dx\) and the analytic theory of numbers,? Acta Math.,61, 323?360 (1933). · Zbl 0008.05501 · doi:10.1007/BF02547795
[463] L. J. Mordell, ?The number of solutions of some congruences in two variables,? Math. Z.,37, 193?209 (1933). · Zbl 0007.00501 · doi:10.1007/BF01474570
[464] L. J. Mordell, ?On recurrent formulae for the number of classes of definite binary quadratic forms,? J. Indian Math. Soc.,24, Nos. 3?4, 367?378 (1960).
[465] C. J. Moreno, ?Prime number theorem for the coefficients of modular forms,? Bull. Am. Math. Soc.,78, No. 5, 796?798 (1972). · Zbl 0274.10031 · doi:10.1090/S0002-9904-1972-13040-4
[466] C. J. Moreno, ?The Hoheisel phenomenon for generalized Dirichlet series,? Proc. Am. Math. Soc.,40, No. 1, 47?51 (1973). · Zbl 0268.10029 · doi:10.1090/S0002-9939-1973-0327682-0
[467] C. J. Moreno, ?A necessary and sufficient conditions for the Riemann hypothesis for Ramanujan’s zeta function,? Ill. J. Math.,18, No. 1, 107?114 (1974). · Zbl 0274.10032
[468] C. J. Moreno, ?Sur le probleme de Kummer,? Enseign. Math.,20, Nos. 1?2, 45?51 (1974).
[469] Mori Mitsuya,? Über die rationale Darstellbarkeit der Heckeschen Operatoren,? J. Math. Soc. Jpn.,15, No. 3, 256?267 (1963). · Zbl 0142.05601 · doi:10.2969/jmsj/01530256
[470] Morita Yasuo, ?Hecke polynomials H k (p) (u) (p=2 or 3),? J. Fac. Sci. Univ. Tokyo,15, Sec. 1, No. 1, 99?105 (1968). · Zbl 0165.54901
[471] Morita Yasuo, ?Hecke polynomials of modular groups and congruence zeta functions of fibre varieties,? J. Math. Soc. Jpn.,21, No. 4, 617?637 (1969). · Zbl 0212.25705 · doi:10.2969/jmsj/02140617
[472] Motohashi Yoichi, ?A new proof of the limit formula of Kronecker,? Proc. Jpn. Acad.,44, No. 7, 614?616 (1968). · Zbl 0186.08301 · doi:10.3792/pja/1195521077
[473] H. Naganuma, ?On the coincidence of two Dirichlet series associated with cusp forms of Hecke’s ?Neben?-type and Hilbert modular forms over a real quadratic field,? J. Math. Soc. Jpn.,25, No. 4, 547?555 (1973). · Zbl 0259.10023 · doi:10.2969/jmsj/02540547
[474] J. von Neumann and H. Goldstine, ?A numerical study of a conjecture of Kummer,? Math. Tables Other Aids Comput.,7, No. 42, 133?134 (1953).
[475] M. F. Newman, ?Remarks on some modular identities,? Trans. Am. Math. Soc,73, 313?320 (1952). · Zbl 0047.04303 · doi:10.1090/S0002-9947-1952-0049934-5
[476] M. F. Newman, ?The coefficients of certain infinite products,? Proc. Am. Math. Soc.,4, No. 3, 435?439 (1953). · Zbl 0050.26901 · doi:10.1090/S0002-9939-1953-0054633-6
[477] M. F. Newman, ?An identity for the coefficients of certain modular forms,? J. London Math. Soc.,30, No. 4, 488?493 (1955). · Zbl 0064.28203 · doi:10.1112/jlms/s1-30.4.488
[478] M. F. Newman, ?On the existence of identities for the coefficients of certain modular forms,? J. London Math. Soc.,31, No. 3, 350?359 (1956). · Zbl 0073.26801 · doi:10.1112/jlms/s1-31.3.350
[479] M. F. Newman, ?Some theorems about pr(n),? Can. J. Math.,9, No. 1, 68?70 (1957). · Zbl 0078.03402 · doi:10.4153/CJM-1957-009-6
[480] M. F. Newman, ?Congruences for the coefficients of modular forms and some new congruences for the partition function,? Can. J. Math.,9, No. 4, 549?552 (1957). · Zbl 0078.03403 · doi:10.4153/CJM-1957-062-1
[481] M. F. Newman, ?Congruences for the coefficients of modular forms and for the coefficients of j(?),? Proc. Am. Math. Soc.,9, No. 4, 609?612 (1958). · Zbl 0087.08302
[482] M. F. Newman, ?Further identities and congruences for the coefficients of modular forms,? Can. J. Math.,10, No. 4, 577?586 (1958). · Zbl 0097.02902 · doi:10.4153/CJM-1958-058-4
[483] M. F. Newman, ?Modular forms whose coefficients possess multiplicative properties. I, II,? Ann. Math.,70, No. 3, 478?489 (1959);75, No. 2, 242?250 (1962). · Zbl 0090.05502 · doi:10.2307/1970326
[484] M. F. Newman, ?Periodicity modulo m and divisibility properties of the partition function,? Trans. Am. Math. Soc.,97, No. 2, 225?236 (1960). · Zbl 0106.03903
[485] M. F. Newman, ?Congruences for the partition function to composite moduli,? Ill. J. Math.,6, No. 1, 59?63 (1962). · Zbl 0147.26602
[486] M. F. Newman, ?Note on partitions modulo 5,? Math. Comput.,21, No. 99, 481?482 (1967).
[487] M. F. Newman, ?Isometric circles of congruence groups,? Am. J. Math.,91, No. 3, 648?656 (1969). · Zbl 0186.08203 · doi:10.2307/2373344
[488] M. F. Newman, ?A table of?(p) modulo p, p prime, 3 ?p ?16,007,? Math. Comput.,27, 215?216 (1973). · doi:10.2307/2005272
[489] D. Niebur, ?An average value for Ramanujan’s?-function,? Bull. London Math. Soc.,4, No. 1, 23?24 (1972). · Zbl 0251.10021 · doi:10.1112/blms/4.1.23
[490] D. Niebur, ?A class of nonanalytic automorphic functions,? Nagoya Math. J.,52, 133?145 (1973). · Zbl 0288.10010 · doi:10.1017/S0027763000015932
[491] D. Niebur, ?A formula for Ramanujan’s ?-function,? Ill. J. Math.,19, No. 3, 448?449 (1975). · Zbl 0301.10025
[492] Niwa Shinj, ?Modular forms of half integral weight and the integral of certain theta functions,? Nagoya Math. J.,56, 147?161 (1975). · Zbl 0303.10027 · doi:10.1017/S0027763000016445
[493] A. P. Ogg, ?Abelian curves of 2-power conductor,? Proc. Cambr. Phil. Soc.,62, No. 2, 143?148 (1966). · Zbl 0163.15403 · doi:10.1017/S0305004100039670
[494] A. P. Ogg, ?Abelian curves of small conductor,? J. Reine Angew. Math.,226, 204?215 (1967). · Zbl 0163.15404
[495] A. P. Ogg, ?On the eigenvalues of Hecke operators,? Math. Ann.,179, No. 2, 101?108 (1969). · Zbl 0169.10102 · doi:10.1007/BF01350121
[496] A. P. Ogg, ?On a convolution of L-series,? Invent. Math.,7, No. 4, 297?312 (1969). · Zbl 0205.50902 · doi:10.1007/BF01425537
[497] A. P. Ogg, ?On product expansions of theta functions,? Proc. Am. Math. Soc.,21, No. 2, 365?368 (1969). · Zbl 0203.35505 · doi:10.1090/S0002-9939-1969-0260673-6
[498] A. P. Ogg, ?Functional equations of modular forms,? Math. Ann.,183, No. 4, 337?340 (1969). · Zbl 0191.38102 · doi:10.1007/BF01350801
[499] A. P. Ogg, Modular Forms and Dirichlet Series, Benjamin, New York (1969). · Zbl 0191.38101
[500] A. P. Ogg, ?On modular forms with associated Dirichlet series,? Ann. Math.,89, No. 1, 184?186 (1969). · Zbl 0206.36803 · doi:10.2307/1970815
[501] A. P. Ogg, ?A remark on the Sato-Tate conjecture,? Invent. Math.,9, No. 3, 198?200 (1970). · Zbl 0219.14013 · doi:10.1007/BF01404324
[502] A. P. Ogg, ?Survey of modular functions of one variable,? Lect. Notes Math.,320, 1?35 (1973). · Zbl 0258.10012 · doi:10.1007/978-3-540-38509-7_1
[503] A. P. Ogg, ?Hyperelliptic modular curves,? Bull. Soc. Math. Fr.,l02, No. 4, 449?462 (1974). · Zbl 0314.10018 · doi:10.24033/bsmf.1789
[504] A. P. Ogg, ?Diophantine equations and modular forms,? Bull. Am. Math. Soc.,81, No. 1, 14?27 (1975). · Zbl 0316.14012 · doi:10.1090/S0002-9904-1975-13623-8
[505] Orihara Akio, ?On the Eisenstein series for the principal congruence subgroups,? Nagoya Math. J.,34, 129?142 (1969). · Zbl 0174.13201 · doi:10.1017/S0027763000024491
[506] M. Ozeki, ?On modular forms whose Fourier coefficients are nonnegative integers with constant term unity,? Math. Ann.,206, No. 3, 187?203 (1973). · Zbl 0266.10021 · doi:10.1007/BF01429207
[507] L. A. Parson, ?Generalized Kloosterman sums and the Fourier coefficients of cusp forms,? Trans. Am. Math. Soc.,217, 329?350 (1976). · Zbl 0324.10018 · doi:10.1090/S0002-9947-1976-0412112-8
[508] W. B. Pennington, ?On the order of magnitude of Ramanujan’s arithmetical function?(n),? Proc Cambr. Phil. Soc.,47, No. 4, 668?678 (1951). · Zbl 0043.04503 · doi:10.1017/S0305004100027122
[509] H. Petersson, ?Konstruktion der sämtlichen Lösungen einer Riemannschen Funktionalgleichung durch Dirichlet-Reihen mit Eulerscher Produktenwicklung. I, II, III,? Math. Ann.,116, 401?412 (1939);117, 39?64; 277?300 (1940/1941). · Zbl 0022.12904 · doi:10.1007/BF01597364
[510] H. Petersson, ?Über Weierstrasspunkte und die expliziten Darstellungen der automorphen Formen von reeller Dimension,? Math. Z.,52, 32?59 (1949). · Zbl 0034.39405 · doi:10.1007/BF02230683
[511] H. Petersson, ?Über Modulfunktionen und Paritionenprobleme,? Abh. Dtsch. Akad. Wiss. Berlin, Kl. Math. Allgem. Naturwiss., No. 2 (1954).
[512] H. Petersson, ?Über die arithmetischen Eigenschaften eines Systems multiplikativer Modulfunktionen von Primzahlstufe,? Acta Math.,95, Nos. 1?2, 57?110 (1956). · Zbl 0071.04101 · doi:10.1007/BF02401098
[513] H. Petersson, ?Über Partitionenprobleme in Verbindung mit Potenzresten nach einem Prirnzahimodul,? Math. Z.,66, No. 3, 241?268 (1956). · Zbl 0072.27002 · doi:10.1007/BF01186612
[514] H. Petersson, ?Explizite Konstruktion der automorphen Orthogonalfunktionen in den multiplikativen Differentialklassen,? Math. Nachr.,16, Nos. 5?6, 343?368 (1957). · Zbl 0091.07702 · doi:10.1002/mana.19570160508
[515] H. Petersson, ?Über Betragmittelwerte und die Fourier-Koeffizienten der ganzen automorphen Formen,? Arch. Math.,9, No. 3, 176?182 (1958). · Zbl 0082.29504 · doi:10.1007/BF01900496
[516] H. Petersson, ?Asymptotic formulae for the Fourier coefficients of multiplicative automorphic functions,? Semin. Analyt. Funct., Vol. 2, Inst. Adv. Study, Princeton, N. J. (1958). · Zbl 0105.28501
[517] H. Petersson, ?Über Darstellungsanzahlen von Primzahlen durch Quadratsummen,? Math. Z.,71, No. 3, 289?307 (1959). · Zbl 0127.27304 · doi:10.1007/BF01181405
[518] H. Petersson, ?Über eine Funktion von G. Lochs und die Diskriminante der elliptischen Funktionen,? Monatsh. Math.,67, No. 3, 243?258 (1963). · Zbl 0158.08503 · doi:10.1007/BF01294966
[519] H. Petersson, ?Über die Eisensteinschen Reihen der Thetagruppe,? Abh. Math. Semin. Univ. Hamburg,31, Nos. 3?4, 166?178 (1967). · Zbl 0155.12202 · doi:10.1007/BF02992396
[520] H. Petersson, ?Über Funktionen mit dem Transformationsverhalten der logarithmitschen Ableitungen automorpher Formen und die Resultatfunktionen des Heckeschen Summationsverfahrens,? Suomalais. Tiedeakat. Toimituks., Sar AI, No. 445 (1969). · Zbl 0181.36502
[521] H. Petersson, ?Über die Primformen der Hauptkongruenzgruppen,? Abh. Math. Semin. Univ. Hamburg,38, 8?31 (1972). · Zbl 0245.10018 · doi:10.1007/BF02996920
[522] W. Pfetzer, ?Die Wirkung der Modulsubstitutionen auf mehrfache Thetareihen zu quadratischen Formen ungerader Variablenzahl,? Arch. Math.,4, Nos. 5?6, 448?454 (1953). · Zbl 0052.08703 · doi:10.1007/BF01899265
[523] A. K. Pizer, ?Type numbers of Eichler orders,? J. Reine Angew. Math.,264, 76?102 (1973). · Zbl 0274.12008
[524] I. I. Pjateckij-Sapiro, ?Reduction of the fields of modular functions and the rings of functions on p-adic manifolds,? Lect. Notes Math.,155, 151?164 (1970). · doi:10.1007/BFb0060323
[525] I. I. Pjateckij-Sapiro, ?Zeta-functions of modular curves,? Lect. Notes Math.,349, 317?360 (1973). · doi:10.1007/978-3-540-37855-6_5
[526] I. I. Pjateckij-Sapiro, ?On the Weil-Jacquet-Langlands theorem,? in: Lie Groups and Their Representations, Budapest (1975), pp. 583?595.
[527] I. I. Pjateckij-Sapiro, ?Euler subgroups,? in: Lie Groups and Their Representations, Budapest (1975), pp. 597?620.
[528] G. Poitou, ?Approximations diophantiennes et groupe modulaire,? Publ. Sci. Univ. Alger.,A1, No. 1, 15?21 (1954). · Zbl 0064.28502
[529] C. Pommerenke, ?Über die Gleichverteilung von Gitterpunkten auf m-dimensionalen Ellipsoiden,? Acta Arithm.,5, No. 2, 227?257 (1959). · Zbl 0089.26802
[530] P. Ponomarev, ?Arithmetic of quaternary quadratic forms,? Aeta Arithm.,29, No. 1, 1?48 (1976). · Zbl 0321.10023
[531] P. Ponomarev, ?A correspondence between quaternary quadratic forms,? Nagoya Math. J.,62, 125?140 (1976). · Zbl 0314.10014 · doi:10.1017/S0027763000024776
[532] H. Rademacher, ?Trends in research: the analytic number theory,? Bull. Am. Math. Soc.,48, 379?401 (1942). · Zbl 0063.06368 · doi:10.1090/S0002-9904-1942-07679-8
[533] H. Rademacher, ?The Ramanujan identities under modular substitutions,? Trans. Am. Math. Soc,51, 609?636 (1942). · Zbl 0060.10006 · doi:10.1090/S0002-9947-1942-0006204-2
[534] H. Rademacher, ?Generalization of the reciprocity formula for Dedekind sums,? Duke Math. J.,21, No. 3, 391?397 (1954). · Zbl 0057.03801 · doi:10.1215/S0012-7094-54-02140-7
[535] H. Rademacher, ?On the transformation of log?(?),? J. Indian Math. Soc,19, No. 1, 25?30 (1955). · Zbl 0064.32703
[536] H. Rademacher, ?Zur Theorie der Dedekindschen Summen,? Math. Z.,63, No. 5, 445?463 (1956). · Zbl 0071.04201 · doi:10.1007/BF01187951
[537] H. Rademacher, ?Some remarks on certain generalized Dedekind sums,? Acta Arithm.,9, No. 1, 97?105 (1964). · Zbl 0128.27101
[538] H. Rademacher, ?Eine Bemerkung über die Heckeschen Operatoren T(n),? Abh. Math. Semin. Univ. Hamburg,31, Nos. 3?4, 149?151 (1967). · Zbl 0159.11401 · doi:10.1007/BF02992393
[539] H. Rademacher, Topics in Analytic Number Theory, Springer, Berlin (1973). · Zbl 0253.10002
[540] H. Rademacher and E. Grosswald, Dedekind Sums, Carus Math. Monograph,16 (1972).
[541] C. Radoux, ?Repartition des valeurs de la fonction? Ramanujan modulo un nombre premier,? Ann. Soc. Sci. Bruxelles, Ser. 1,.89, No. 4, 434?438 (1975). · Zbl 0314.10019
[542] J. Raleigh, ?The Fourier coefficients of the invariants j(21/2;?) and j (3/2;?),? Trans. Am. Math. Soc.,87, No. 1, 90?107 (1958). · Zbl 0083.04501
[543] J. Raleigh, ?On the Fourier coefficients of triangle functions,? Acta Arithm.,8, No. 1, 107?111 (1962). · Zbl 0113.06603
[544] K. Ramachandra, ?Some applications of Kronecker’s limit formulas,? Ann. Math.,80, No. 1, 104?148 (1964). · Zbl 0142.29804 · doi:10.2307/1970494
[545] K. Ramachandra, ?On the class number of relative Abelian fields,? J. Reine Angew. Math.,236, 1?10 (1969). · Zbl 0175.04601
[546] S. Ramanujan, ?On certain arithmetical functions,? Trans. Cambr. Phil. Soc.,22, 159?184 (1916).
[547] S. Ramanujan, ?Some properties of p(n), the number of partitions of n,? Proc. Cambr. Phil. Soc.,19, 207?210 (1919). · JFM 47.0885.01
[548] S. Ramanujan, ?Congruence properties of partitions,? Math. Z.,9, 147?153 (1921). · JFM 48.0150.02 · doi:10.1007/BF01378341
[549] S. S. Rangachari, ?Modulare Korrespondenzen und L-Reihen,? J. Reine Angew. Math.,205, Nos. 3?4, 119?155 (1961).
[550] R. A. Rankin, ?Contributions to the theory of Ramanujan’s function?(n) and similar arithmetical functions. I. The zeros of the function \(\sum\limits_{n = 1}^\infty {\tau (n)n^{ - s} } \) on the line \(\operatorname{Re} s = \frac{{13}}{2}\) . II. The order of the Fourier coefficients of the integral modular forms. III. A note on the sum function of the Fourier coefficients of integral modular forms,? Proc. Cambr. Phil. Soc.,35, No. 3, 351?356, 357?372 (1939);36, No. 2, 150?151 (1940). · doi:10.1017/S0305004100021095
[551] R. A. Rankin, ?The scalar product of modular forms,? Proc. London Math. Soc., Ser. 3,2, No. 6, 198?217 (1952). · Zbl 0049.33904 · doi:10.1112/plms/s3-2.1.198
[552] R. A. Rankin, ?On horocyclic groups,? Proc. London Math. Soc.,4, No. 14, 219?235 (1954). · Zbl 0055.07602 · doi:10.1112/plms/s3-4.1.219
[553] R. A. Rankin, ?The construction of automorphic forms from the derivatives of a given form,? J. Indian Math. Soc.,20, Nos. 1?3, 103?116 (1956). · Zbl 0072.08601
[554] R. A. Rankin, ?Diophantine approximation and horocyclic groups,? Can. J. Math.,9, No. 2, 277?290 (1957). · Zbl 0082.04002 · doi:10.4153/CJM-1957-034-7
[555] R. A. Rankin, ?Multiplicative functions and operators of Hecke type,? Acta Math. Acad. Sci. Hung.,13, Nos. 1?2, 81?89 (1962). · Zbl 0104.05403 · doi:10.1007/BF02033627
[556] R. A. Rankin, ?On the representation of a number as the sum of any number of squares, and in particular of twenty,? Acta Arithm.,7, No. 4, 399?407 (1962). · Zbl 0106.03804
[557] R. A. Rankin, ?Sums of squares and cusp forms,? Am. J. Math.,87, No. 4, 857?860 (1965). · Zbl 0132.30802 · doi:10.2307/2373249
[558] R. A. Rankin, ?Isomorphic congruence groups and Hecke operators,? Proc. Glasgow Math. Assoc,7, No. 3, 168 (1966). · Zbl 0171.28901 · doi:10.1017/S2040618500035358
[559] R. A. Rankin, ?Hecke operators on congruence subgroups of the modular group,? Math. Ann.,168, 40?58 (1967). · Zbl 0145.32001 · doi:10.1007/BF01361544
[560] R. A. Rankin, ?An ?-result for the coefficients of cusp forms,? Math. Ann.,203, No. 3, 239?250 (1973). · Zbl 0254.10021 · doi:10.1007/BF01629259
[561] R. A. Rankin and J. M. Rushforth,, ?The coefficients of certain integral modular forms,? Proc. Cambr. Phil. Soc.,50, No. 2, 305?308 (1954). · Zbl 0057.31603 · doi:10.1017/S0305004100029376
[562] H. L. Resnikoff, ?On differential operators and automorphic forms,? Trans. Am. Math. Soc.,124, 334?346 (1966). · Zbl 0148.32504 · doi:10.1090/S0002-9947-1966-0204651-3
[563] K. A. Ribet, ?On t-adic representations attached to modular forms,? Invent. Math.,28, No. 3, 245?275 (1975). · Zbl 0302.10027 · doi:10.1007/BF01425561
[564] D. E. Rideout, ?A simplification of the formula for L(1, ?) where ? is a totally imaginary Dirichlet character of a real quadratic field,? Acta Arithm.,23, No. 4, 329?337 (1973). · Zbl 0269.10023
[565] G. J. Rieger, ?Dedekindsche Summen in algebraischen Zahlkör pern,? Math. Ann.,141, No. 5, 377?383 (1960). · Zbl 0131.03603 · doi:10.1007/BF01360254
[566] Ø. Rødseth, ?Dissections of the generating functions of q (n) and q0(n),? Arb. Univ. Bergen Mat.-Naturvit. Ser., No. 12, 1?12 (1969).
[567] Ø. Rødseth, ?Congruence properties of the partition functions q (n) and q0(n),? Arb. Univ. Bergen Mat.Naturvit. Ser., No. 13, 1?27 (1969).
[568] W. Roelcke, ?Über die Verteilung der Klassen eigentlich assoziierter zweireihiger Matrizen die sich durch eine positiv-definite Matrix darstellen lassen,? Math. Ann.,131, No. 3, 260?277 (1956). · Zbl 0071.07801 · doi:10.1007/BF01342964
[569] W. Roelcke, ?Über die Verteilung der zweiten Zeilen der Matrizen gewisser Grenzkreisgruppen,? Math. Ann.,141, No. 4, 367?376 (1960). · Zbl 0095.28201 · doi:10.1007/BF01360768
[570] H. Roth, ?Sur un theoreme de Maillet,? Bull. Sci. Math.,86, No. 2, 61?63 (1962). · Zbl 0107.27001
[571] Saito Hiroshi, ?On Eichler’s trace formula,? J. Math. Soc. Jpn.,24, No. 2, 333?340 (1972). · Zbl 0232.10019 · doi:10.2969/jmsj/02420333
[572] Saito Hiroshi, ?Automorphic forms and algebraic extensions of number fields,? Proc. Jpn. Acad.,51, No. 4, 229?233 (1975). · Zbl 0317.10039 · doi:10.3792/pja/1195518624
[573] Saito Hiroshi, ?Automorphic forms and algebraic extensions of number fields,? Lectures in Mathematics, Department of Mathematics, Kyoto Univ., No. 8 (1975). · Zbl 0317.10039
[574] A. C. Schaeffer, ?Dirichlet series,? Ill. J. Math.,4, No. 4, 479?500 (1960). · Zbl 0111.05001
[575] R. Schertz, ?L-Reihen in imaginärquadratischen Zahlkörpern und ihre Anwendung auf Klassenzahlprobleme bei quadratischen und biquadratischen Zahlkörpern. I, II,? J. Reine Angew. Math.,262?263, 120?133 (1973);270, 195?212 (1974). · Zbl 0285.12015
[576] R. Schertz, ?Arithmetische Ausdeutung der Klassenzahlformel für einfach reelle kubische Zahlkörper,? Abh. Math. Semin. Univ. Hamburg,41, 211?223 (1974). · Zbl 0364.12002 · doi:10.1007/BF02993515
[577] B. Schoeneberg, ?Über den Zusammenhang der Eisensteinsche Reihen und Thetareihen mit der Diskriminante der elliptischen Funktionen,? Math. Ann.,126, No. 3, 177?184 (1953). · Zbl 0053.05403 · doi:10.1007/BF01343159
[578] B. Schoeneberg, ?Über die Quaternionen in der Theorie der elliptischen Modulfunktionen,? J. Reine Angew. Math.,193, Nos. 1?2, 84?93 (1954). · Zbl 0055.31201
[579] B. Schoeneberg, ?Über die Diskriminante der elliptischen Funktionen und ihre Quadratwurzel,? Math. Z.,65, No. 1, 16?24 (1956). · Zbl 0071.07901 · doi:10.1007/BF01473867
[580] B. Schoeneberg, ?Über die Eisensteinschen Reihen von Primzahlstufe,? Abh. Math. Semin. Univ. Hamburg,26, Nos. 3?4, 145?154 (1964). · Zbl 0125.04301 · doi:10.1007/BF02992784
[581] B. Schoeneberg, ?Zur Theorie der verallgemeinerten Dedekindschen Modulfunktionen, mationen und verallgemeinerte Dedekindsche Summen,? Abh. Math. Semin. Univ. Hamburg,30, Nos, 1?2, 1?10 (1967). · Zbl 0158.08602 · doi:10.1007/BF02993987
[582] B. Schoeneberg, ?Bemerkungen über einige Klassen von Modulformen,? Proc. K. Ned. Akad. Wet.,A70, No. 2, 177?182 (1967); Indag. Math.,29, No. 2, 177?182 (1967).
[583] B. Schoeneberg, ?Zur Theorie der verallgemeinerten Dedekindschen Modulfunktionen,? Nachr. Akad. Wiss. Gottingen. II Math.-Phys. Kl., No. 13 (1969). · Zbl 0197.32402
[584] B. Schoeneberg, ?Elliptic Modular Functions. An Introduction, Springer, Berlin (1974). · Zbl 0285.10016
[585] A. Selberg, ?Bemerkungen über eine DirichletscheReiche, diemitder Theorie der Modulformen nahe verbunden ist,? Arch. Math. Naturvid.,43, 47?50 (1940). · JFM 66.0377.01
[586] A. Selberg, ?Harmonic analysis and discontinuous groups in weakly symmetric Riemannian spaces with applications to Dirichlet series,? J. Indian Math. Soc.,20, Nos. 1?3, 47?87 (1956). · Zbl 0072.08201
[587] A. Selberg, ?Automorphic functions and Integral operations,? in: Semin. Analyt. Funct., Vol. 2, Inst. Adv. Study, Princeton, N. J. (1958), pp. 152?161.
[588] A. Selberg, ?Discontinuous groups and harmonic analysis,? in: Proc. Int. Congr. Math. Aug. 1962, Djursholm, Uppsala (1963), pp. 177?189.
[589] A. Selberg, ?On the estimation of Fourier coefficients of modular forms,? in: Proc. Sympos. Pure Math., Vol. 8, Number Theory, Providence, R.I. (1965), pp. 1?15. · Zbl 0142.33903
[590] A. Selberg and S. Chowla, ?On Epstein’s zeta function,? J. Reine Angew. Math.,227, 86?110 (1967). · Zbl 0166.05204
[591] A. Borel, S. Chowla, C. S. Herz, K. Iwasawa, and J. P. Serre, Seminar on Complex Multiplication, Lect. Notes Math.,21 (1966). · Zbl 0147.03902
[592] J. P. Serre, Abelian ?-Adic Representations and Elliptic Curves, Benjamin, New York (1968). · Zbl 0186.25701
[593] J. P. Serre, ?Une interpretation des congruences relatives a la fonction? de Ramanujan,?Semin. Theor, Nombres Delange-Pisot-Poitou, Fac. Sci. Paris, 1967?1968,9, No. 1, 14/01?14/17 (1969).
[594] J. P. Serre, Cours d’Arithmetique, Presses Univ. de France, Paris (1970).
[595] J. P. Serre, ?Congruences et formes modulaires (d’apres H. P. F. Swinnerton-Dyer),? Lect. Notes Math.,317, 319?338 (1973). · Zbl 0276.14014 · doi:10.1007/BFb0069289
[596] J. P. Serre, ?Formes modulaires et fonctions zeta p-adiques,? Lect. Notes Math.,350, 191?268 (1973). · Zbl 0277.12014 · doi:10.1007/978-3-540-37802-0_4
[597] J. P. Serre, ?Divisibilite des coefficients des formes modulaires de poids entiers,? C. R. Acad. Sci.,A279, No. 17, 679?682 (1974). · Zbl 0304.10017
[598] J. P. Serre, ?Divisibilite de certaines fonctions arithmetiques,? Semin. Delange ?Pisot?Poitou, Theor. Nombres, Univ. Pierre et Marie Curie, 1974?1975,16, No. 1, 20/1?20/28; Enseign. Math.,22, Nos. 3?4, 227?260 (1976).
[599] J. P. Serre, ?Valeurs propres des operateurs de Hecke modulo l,? Asterisque, Nos. 24?25, 109?117 (1975).
[600] L. Seshu, ?On the simultaneous representation of a given pair of integers as the sum, respectively, of four integers and their squares. I, II,? Proc. K. Ned. Akad. Wet.,A64, No. 1, 64?79, 80?88 (1961); Indag. Math.,23, No. 1, 64?79, 80?88 (1961). · Zbl 0116.27004
[601] J. A. Shalika, ?Some conjectures in class field theory,? in: Proc. Sympos. Pure Math., Vol. 20, Number Theory, Providence, R.I. (1971), pp. 115?122. · Zbl 0231.12016 · doi:10.1090/pspum/020/0345935
[602] J. A. Shalika and S. Tanaka, ?On an explicit construction of a certain class of automorphic forms,? Am. J. Math.,91, No. 4, 1049?1076 (1969). · Zbl 0217.43302 · doi:10.2307/2373316
[603] D. Shanks, ?Calculation and applications of Epstein zeta functions,? Math. Comput.,29, No. 129, 271?287 (1975). · Zbl 0302.10035 · doi:10.1090/S0025-5718-1975-0409357-2
[604] Shimizu Hideo, ?On discontinuous groups operating on the product of the upper half planes,? Ann. Math.,77, No. 1, 33?71 (1963). · Zbl 0218.10045 · doi:10.2307/1970201
[605] Shimizu Hideo, ?On traces of Hecke operators,? J. Fac. Sci. Univ. Tokyo, Sec. 1,10, No. 1, 1?19 (1963). · Zbl 0142.05502
[606] Shimizu Hideo, ?On zeta functions of quaternion algebras,? Ann. Math.,81, No. 1, 166?193 (1965). · Zbl 0201.37903 · doi:10.2307/1970389
[607] Shimizu Hideo, ?Theta series and automorphic forms on GL2,? J. Math. Soc. Jpn.,24, No. 4, 638?683 (1972); errata: ibid.,26, No. 2, 374?376 (1974). · Zbl 0241.10016 · doi:10.2969/jmsj/02440638
[608] Shimura Goro, ?Correspondances modulaires et les fonctions ? de courbes algebriques,? J. Math. Soc. Jpn.,10, No. 1, 1?28 (1958). · Zbl 0081.07603 · doi:10.2969/jmsj/01010001
[609] Shimura Goro, ?Sur les integrales attachees aux formes automorphes,? J. Math. Soc. Jpn.,11, No. 4, 291?311 (1959). · Zbl 0090.05503 · doi:10.2969/jmsj/01140291
[610] Shimura Goro, ?On the zeta-functions of the algebraic curves uniformized by certain automorphic functions,? J. Math. Soc. Jpn.,13, No. 3, 275?331 (1961). · Zbl 0218.14013 · doi:10.2969/jmsj/01330275
[611] Shimura Goro, ?On Dirichlet series and Abelian varieties attached to automorphic forms,? Ann. Math.,76, No. 2, 237?294 (1962). · Zbl 0142.05501 · doi:10.2307/1970275
[612] Shimura Goro, ?The zeta-function of an algebraic variety and automorphic functions,? Lect. Notes Am. Math. Soc. and Summer Inst. Algebr. Geometry, Woods Hole, Mass. (1964), pp. 1?23.
[613] Shimura Goro, ?A reciprocity law in non-solvable extensions,? J. Reine Angew. Math.,221, 209?220 (1966). · Zbl 0222.14027
[614] Shimura Goro, ?Construction of class fields and zeta functions of algebraic curves,? Ann. Math.,85, No. 1, 58?159 (1967). · Zbl 0204.07201 · doi:10.2307/1970526
[615] Shimura Goro, ?Automorphic functions and number theory,? Lect. Notes Math.,54, VI (1968). · Zbl 0183.25402
[616] Shimura Goro, ?Class fields over real quadratic fields in the theory of modular functions,? Lect. Notes Math.,185, 169?188 (1971). · Zbl 0255.10031 · doi:10.1007/BFb0058770
[617] Shimura Goro, Introduction to the Arithmetic Theory of Automorphic Functions, Iwanami Shoten Publ. and Princeton Univ. Press (1971). · Zbl 0221.10029
[618] Shimura Goro, ?Modular forms of half integral weight,? Lect. Notes Math.,320, 57?74 (1973). · Zbl 0266.10022 · doi:10.1007/978-3-540-38509-7_3
[619] Shimura Goro, ?On modular forms of half integral weight,? Ann. Math.,97, No. 3, 440?481 (1973). · Zbl 0266.10022 · doi:10.2307/1970831
[620] Shimura Goro, ?Complex multiplication,? Lect. Notes Math.,320, 37?56 (1973). · Zbl 0268.10015 · doi:10.1007/978-3-540-38509-7_2
[621] Shimura Goro, ?On the trace formula for Hecke operators,? Acta Math.,132, Nos. 3?4, 245?281 (1974). · Zbl 0285.10018 · doi:10.1007/BF02392117
[622] Shimura Goro, ?On the holomorphy of certain Dirichlet series,? Proc. London Math. Soc.,31, No. 1, 79?98 (1975). · Zbl 0311.10029
[623] Shimura Goro, ?On some arithmetic properties of modular forms of one and several variables,? Ann. Math.,102, No. 3, 491?515 (1975). · Zbl 0327.10028 · doi:10.2307/1971041
[624] Shimura Goro, ?On the Fourier coefficients of modular forms of several variables,? Nachr. Akad. Wiss. Gottingen. II Math.-Phys. Kl., No. 17, 261?268 (1975). · Zbl 0332.32024
[625] Shintani Takuro, ?On zeta-functions associated with the vector space of quadratic forms,? J. Fac. Sci. Univ. Tokyo, Sec. 1A,22., No. 1, 25?65 (1975). · Zbl 0313.10041
[626] Shintani Takuro, ?On construction of holomorphic cusp forms of half integral weight,? Nagoya Math. J.,58, 83?126 (1975). · Zbl 0316.10016 · doi:10.1017/S0027763000016706
[627] Shintani Takuro, ?On evaluation of zeta functions of totally real algebraic number fields at non-positive integers,? J. Fac. Sci. Univ. Tokyo, Sec. 1A,23, No. 2, 393?417 (1976). · Zbl 0349.12007
[628] C. L. Siegel, ?Über die analytische Theorie der quadratischen Formen,? Ann. Math.,36, No. 3, 527?606 (1935). · JFM 61.0140.01 · doi:10.2307/1968644
[629] C. L. Siegel, ?Über die Zetafunktionen indefiniter quadratischer Formen,? Math. Z.,43, No. 5, 682?708 (1938). · JFM 64.0976.03 · doi:10.1007/BF01181113
[630] C. L. Siegel, ?Die Funktionalgleichungen einiger Dirichletscher Reihen,? Math. Z.,63, No. 4, 363?373 (1956). · Zbl 0070.07702 · doi:10.1007/BF01187948
[631] C. L. Siegel, Lectures on Quadratic Forms, Tata Inst. Fund. Research, Bombay (1957). · Zbl 0248.10019
[632] C. L. Siegel, Lectures on Advanced Analytic Number Theory, Tata Inst. Fund. Research, Bombay (1961).
[633] C. L. Siegel, Lectures on the Analytic Theory of Quadratic Forms, 3rd rev. ed., Peppmüller, Göttingen (1963). · Zbl 0115.04401
[634] C. L. Siegel, ?Zum Beweise der Starkschen Satzen,? Invent. Math.,5, No. 3, 180?191 (1968). · Zbl 0175.33602 · doi:10.1007/BF01425549
[635] C. L. Siegel, ?Bernoullische Polynome und quadratischen Zahlkörper,? Nachr. Akad. Wiss. Göttingen, II, Math.-Phys. Kl. 1968, pp. 7?38. · Zbl 0273.12002
[636] C. K. Siegel, ?Berechnung von Zetafunktionen an ganzzahligen Stellen,? Nachr. Akad. Wiss. Göttingen. II Math.-Phys. Kl. No. 10 (1969). · Zbl 0186.08804
[637] C. L. Siegel, ?Über die Fourierschen Koeffizienten von Modulformen,? Nachr. Akad. Wiss. Göttingen. II Math.-Phys. Kl. No. 3 (1970). · Zbl 0225.10031
[638] J. R. Smart, ?A basis theorem for cusp forms on groups of genus zero,? Mich. Math. J.,10, No. 4, 375?380 (1963). · Zbl 0122.32101 · doi:10.1307/mmj/1028998973
[639] J. R. Smart, ?On modular forms of dimension-2,? Trans. Am. Math. Soc.,116, No. 4, 86?107 (1965). · Zbl 0144.08302
[640] J. R. Smart, ?On Weierstrass points in the theory of elliptic modular forms,? Math. Z.,94, No. 3, 207?218 (1966). · Zbl 0148.32601 · doi:10.1007/BF01111349
[641] J. R. Smart, ?On the values of the Epstein zeta function,? Glasgow Math. J.,14, No. 1, 1?12 (1973). · Zbl 0254.10036 · doi:10.1017/S001708950000166X
[642] R. Spira, ?Calculation of the Ramanujan?-Dirichlet series,? Math. Comput.,27, No. 122, 379?385 (1973). · Zbl 0283.10022
[643] H. M. Stark, ?A complete determination of complex quadratic fields of class-number one,? Mich. Math. J.,14, No. 1, 1?27 (1967). · Zbl 0148.27802 · doi:10.1307/mmj/1028999653
[644] H. M. Stark, ?L-Functions and character sums for quadratic forms. I, II,? Acta Arithm.,14, No. 1, 35?50 (1968);15, No. 3, 307?317 (1969).
[645] H. M. Stark, ?The role of modular functions in a class-number problem,? J. Number Theory,1, No. 2, 252?260 (1969). · Zbl 0198.07402 · doi:10.1016/0022-314X(69)90044-4
[646] H. M. Stark, ?A historical note on complex quadratic fields with class-number one,? Proc. Am. Math. Soc,21, No. 1, 254?255 (1969). · Zbl 0191.33401
[647] H. M. Stark, ?On the ?Gap? in a theorem of Heegner,? J. Number Theory,1, No. 1, 16?27 (1969). · Zbl 0198.37702 · doi:10.1016/0022-314X(69)90023-7
[648] H. M. Stark, ?Class-number problems in quadratic fields,? Actes Congr. Int. Mathematiciens, 1970, T. 1, Paris, 1971, pp. 511?518.
[649] H. M. Stark, ?Recent advances in determining all complex quadratic fields of a given class-number,? Proc. Sympos. Pure Math., Vol. 20, Number Theory, Providence, R. I. (1971), pp. 401?414. · Zbl 0231.12008
[650] H. M. Stark, ?A transcendence theorem for class-number problems. I, II,? Ann. Math.,94, No. 1, 153?173 (1971);96, No. 1, 174?209 (1972). · Zbl 0229.12010 · doi:10.2307/1970740
[651] H. M. Stark, ?Values of L-functions at s=1. I. L-Functions for quadratic forms. II. Artin L-functions with rational characters,? Adv. Math.,7, No. 3, 301?343 (1971);17, No. 1, 60?92 (1975). · Zbl 0263.10015 · doi:10.1016/S0001-8708(71)80009-9
[652] H. M. Stark, ?Class-numbers of complex quadratic fields,? Lect. Notes Math.,320, 153?174 (1973). · Zbl 0259.10026 · doi:10.1007/978-3-540-38509-7_5
[653] H. M. Stark, ?Review of ?Topics in analytic number theory? by Hans Rademacher,? Bull. Am. Math. Soc,81, No. 4, 663?672 (1975). · doi:10.1090/S0002-9904-1975-13815-8
[654] H. M. Stark, ?On complex quadratic fields with class-number two,? Math. Comput.,29, No. 129, 289?302 (1975). · Zbl 0321.12009
[655] H. P. F. Swinnerton-Dyer, ?On l-adic representations and congruences for coefficients of modular forms,? Lect. Notes Math.,350, 1?55 (1973). · doi:10.1007/978-3-540-37802-0_1
[656] T. Tatuzawa, ?On the extended Hecke theta-formula,? Tr. Mat. Inst. Akad. Nauk SSSR,132, 206?211 (1973). · Zbl 0292.12014
[657] A. Terras, ?Bessel series expansions of the Epstein zeta function and the functional equation,? Trans. Am. Math. Soc.,183, 477?486 (1973). · Zbl 0274.10039 · doi:10.1090/S0002-9947-1973-0323735-6
[658] A. Terras, ?Fourier coefficients of Eisenstein series of one complex variable for the special linear group,? Trans. Am. Math. Soc,205, 97?114 (1975). · Zbl 0303.10029
[659] A. Terras, ?Some formulas for the Riemann zeta function at odd integer argument resulting from Fourier expansions of the Epstein zeta function,? Acta Arithm.,29, No. 2, 181?189 (1976). · Zbl 0282.10025
[660] A. Terras, ?The Fourier expansion of Epstein’s zeta function for totally real algebraic number fields and some consequences for Dedekind’s zeta function,? Acta Arithm.,30, No. 2, 187?197 (1976). · Zbl 0295.12006
[661] L. Tornheim, ?Approximation to irrationals by classes of rational numbers,? Proc. Am. Math. Soc.,6, No. 2, 260?264 (1955). · Zbl 0064.28503 · doi:10.1090/S0002-9939-1955-0068590-1
[662] Uehara Tsuyoshi, ?Bernoulli numbers in real quadratic fields (a remark on a work of H. Lang),? Repts. Fac. Sci. and Eng. Saga Univ. Math., No. 4, 1?5 (1976). · Zbl 0333.12006
[663] B. van der Pol, ?On a non-linear differential equation satisfied by the logarithm of the Jacobian theta functions, with arithmetical applications. I, II,? Indag. Math.,13, 261?284 (1951).
[664] Rao V. Venugopal, ?Functional equations of Diriehlet series derived from non-analytic automorphic forms of a certain type,? Can. Math. Bull.,18, No. 1, 87?94 (1975). · Zbl 0312.10015 · doi:10.4153/CMB-1975-016-9
[665] D. -N. Verma, ?Review of I. G. Macdonald’s paper ?Affine root systems and Dedekind’s ?-function,?? Math. Reviews,50, No. 5, 1371?1374 (1975).
[666] M.-F. Vigneras-Gueho, ?Partie fractionaire de zeta au point-1,? C. R. Acad. Sci.,A279, No. 10, 359?361 (1974).
[667] M.-F. Vigneras-Gueho, ?Nombre de classes d’un ordre d’Eichler et valeur au point-1 de la fonction zeta d’un corps quadratique reel,? Enseign. Math.,21, No. 1, 69?105 (1975).
[668] Wada Hideo, ?A table of Hecke operators. I, II,? in: United States-Japan Seminar on Modern Methods in Number Theory, Tokyo Univ. (1971), pp. 1?10; Proc. Jpn. Acad.,49, No. 6, 380?384 (1973).
[669] A. Walficz,?Über die Koeffizientensummen einiger Modulformen,? Math. Ann.,108, 75?90 (1933). · JFM 59.0213.02 · doi:10.1007/BF01452823
[670] A. Walficz, ?Über die Koeffizienten einiger Modulformen,? Prac. Matematyczno-Fizycznych,40, 149?155 (1933).
[671] Watabe Mutsuo, ?On Fourier coefficients of certain cusp forms,? Proc. Jpn. Acad.,49, No. 8, 578?582 (1973). · Zbl 0284.10008 · doi:10.3792/pja/1195519219
[672] G. N. Watson, ?Ramanujan Vermutung über Zerfallungsanzahlen,? J. Reine Angew. Math.,179, 97?128 (1938).
[673] A. Weil, ?Sur certains groupes d’operateurs unitaires,? Acta Math.,111, Nos. 3?4, 143?211 (1964). · Zbl 0203.03305 · doi:10.1007/BF02391012
[674] A. Weil, ?Sur la formule de Siegel dans la theorie des groupes classiques,? Acta Math.,113, Nos. 1?2, 1?87 (1965). · Zbl 0161.02304 · doi:10.1007/BF02391774
[675] A. Weil, ?Über die Bestimmung Dirichletscher Reihen durch Funktionalgleichungen,? Math. Ann.,168, 149?156 (1967). · Zbl 0158.08601 · doi:10.1007/BF01361551
[676] A. Weil, ?Sur une formule classique,? J. Math. Soc. Jpn.,20, Nos. 1?2, 400?402 (1968). · Zbl 0174.33902 · doi:10.2969/jmsj/02010400
[677] A. Weil, ?Zeta-functions and Mellin transforms,? Algebr. Geom. London, 1969, pp. 409?426.
[678] A. Weil, ?Dirichlet series and automorphic forms,? Lect. Notes Math.,189 (1971). · Zbl 0218.10046
[679] A. van Wijngaarden, ?On the coefficients of the modular invariant J(?),? Proc. Kon. Ned. Akad. Wet.,A56, No. 4, 389?400 (1953); Indag. Math.,15, No. 4, 389?400 (1953). · Zbl 0051.31803
[680] J. R. Wilton, ?A note on Ramanujan’s arithmetical function? (n),? Proc. Cambr. Phil. Soc.,25, 121?129 (1929). · JFM 55.0709.02 · doi:10.1017/S0305004100018636
[681] J. R. Wilton, ?Congruence properties of Ramanujan’s function? (n),? Proc. London Math. Soc.,31, 1?10 (1930). · JFM 56.0874.02 · doi:10.1112/plms/s2-31.1.1
[682] L. Winquist, ?An elementary proof of p(11m + 6) ? 0 (mod 11),? J. Combin. Theory,6, No. 1, 56?59 (1969). · Zbl 0241.05006 · doi:10.1016/S0021-9800(69)80105-5
[683] R.-D. Wirsching, ?Ramanujan-Identitäten zur Reziproken der Jacobischen Funktion ?,? J. Reine Angew. Math.,264, 149?160 (1973). · Zbl 0267.10036
[684] E. Witt, ?Identität zwischen Modulformen zweiten Grades,? Abh. Math. Semin. Univ. Hamburg,14, 323?337 (1941). · Zbl 0025.01701 · doi:10.1007/BF02940750
[685] K. Wohlfahrt, ?Über Operatoren Heckescher Art bei Modulformen reeller Dimension,? Math. Nachr.,16, Nos. 3?4, 233?256 (1957). · Zbl 0080.06101 · doi:10.1002/mana.19570160307
[686] K. Wohlfahrt, ?Über Dedekindsche Summen und Untergruppen der Modulgruppe,? Abh. Math. Seminar Univ. Hamburg,23, 5?10 (1959). · Zbl 0086.06702 · doi:10.1007/BF02941021
[687] K. Wohlfahrt, ?Eine Anwendung von?(?),? J. Number Theory,2, No. 3, 273?278 (1970). · Zbl 0197.32804 · doi:10.1016/0022-314X(70)90054-5
[688] Yamada Toshihiko, ?On the distribution of the norms of the hyperbolic transformations,? Osaka J. Math.,3, No. 1, 29?37 (1966). · Zbl 0186.40601
[689] Yamauchi Masatoshi, ?Some identities on the character sum containing x(x ?1) (x ??),? Nagoya Math. J.,42, 109?113 (1971). · Zbl 0219.14015 · doi:10.1017/S0027763000014288
[690] Yamauchi Masatoshi, ?On the trace of Hecke operators for certain modular groups,? Nagoya Math. J.,43, 137?149 (1971). · Zbl 0224.10026 · doi:10.1017/S0027763000014410
[691] Yoshida Hiroyuki, ?On an analogue of the Sato conjecture,? Invent. Math.,19, No. 4, 261?277 (1973). · Zbl 0292.14011 · doi:10.1007/BF01425416
[692] D. Zagier, ?Higher dimensional Dedekind sums,? Math. Ann.,202, No. 2, No. 2, 149?172 (1973). · Zbl 0237.10025 · doi:10.1007/BF01351173
[693] D. Zagier, ?Formes modulaires a une et deux variables,? C. R. Acad. Sci.,A279, No. 17, 683?686 (1974). · Zbl 0293.10013
[694] D. Zagier, ?A Kronecker limit formula for real quadratic fields,? Math. Ann.,213, No. 2, 153?184 (1975). · Zbl 0283.12004 · doi:10.1007/BF01343950
[695] D. Zagier, ?Modular forms associated to real quadratic fields,? Invent. Math.,30, No. 1, 1?46 (1975). · Zbl 0308.10014 · doi:10.1007/BF01389846
[696] D. Zagier, ?Nombres de classes et formes modulaires de poids 3/2,? C. R. Acad. Sci.,A281, No. 21, 883?886 (1975). · Zbl 0323.10021
[697] D. Zagier, ?Nombres de classes et fractions continues,? Asterisque, Nos. 24?25, 81?97 (1975).
[698] D. Zagier, ?On the values at negative integers of the zeta-function of a real quadratic field,? Enseign. Math.,22, Nos. 1?2, 55?95 (1976). · Zbl 0334.12021
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.