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Kloosterman sums and Fourier coefficients of cusp forms. (English) Zbl 0502.10021

11L05 Gauss and Kloosterman sums; generalizations
11F30 Fourier coefficients of automorphic forms
11F11 Holomorphic modular forms of integral weight
11N35 Sieves
11N37 Asymptotic results on arithmetic functions
11M06 \(\zeta (s)\) and \(L(s, \chi)\)
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[1] [Bru] Bruggeman, R.W.: Fourier coefficients of cusp forms. Invent. Math.45, 1-18 (1978) · Zbl 0363.10018
[2] [Bus] Buser, P.: On Cheeger’s inequality? 1?h 2/4. Proc. Symposia, in Pure Math., XXXVI, pp. 29-77 AMS, Providence 1981
[3] [Che] Cheeger, J.: A lower bound for the smallest eigenvalue of the Laplacian. Problems in Analysis, A symposium in honour of Bochner, Princeton University Press, Princeton, N.J. 1970 pp. 195-199
[4] [Del] Deligne, P.: La conjecture de Weil I. Publ. Math. I.H.E.S.,43, 273-307 (1974)
[5] [Dl 1] Deshouillers, J.-M., Iwaniec, H.: On the greatest prime factor ofn 2+1 Ann. Inst. Fourier. in press (1982) · Zbl 0489.10038
[6] [DI2] Deshouillers, J.-M., Iwaniec, H.: An additive divisor problem. J. London Math. Soc.26, (2), 1-14 (1982) · Zbl 0488.10044
[7] [Di3] Deshouillers, J.-M., Iwaniec, H.: Power mean-values for the Riemann zeta-function. Mathematika in press (1982) · Zbl 0506.10032
[8] [DI4] Deshouillers, J.-M., Iwaniec, H.: On the Brun-Titchmarsh theorem and the greatest prime factor ofp+a. Proc. Janos Bolyai Soc. Conf. in press (1982)
[9] [EMOT] Erdélyi, A., Magnus, W., Oberhettinger, F., Tricomi, F.G.: Higher Transcendental Functions II. New York-Toronto-London: Mc Graw-Hill 1953 · Zbl 0052.29502
[10] [Fad] Faddeev, L.D.: Expansions in eigenfunctions of the Laplace operator in the fundamental domain of a discrete group on the Loba?evskii plane. Trudy Moscov, Mat. Obsc.,17, 323-350 (1967) · Zbl 0201.41601
[11] [G-R] Gradsztejn, I.S., Ry?yk, I.M.: Tablice ca?ek, sum, szeregów i iloczynow. PWN-Warszawa, 1964
[12] [Gun] Gunning, R.C.: Lectures on modular forms. Princeton University Press, 1962 · Zbl 0178.42901
[13] [H.-B.] Heath-Brown, D.R.: The fourth power moment of the Riemann zeta-function. Proceeding London Math. Soc.38(3), 385-422 (1979) · Zbl 0403.10018
[14] [Hej] Hejhal, D.A.: Some observations concerning eigenvalues of the Laplacian and DirichletL-series in Recent progress in analytic number theory. London: Academic Press 1981
[15] [Hoo] Hooley, C.: On the greatest prime factor of a quadratic polynomial. Acta Math.117, 281-299 (1967) · Zbl 0146.05704
[16] [Iwa 1] Iwaniec, H.: Fourier coefficients of cusp forms and the Riemann zeta-function. Sém. Th. Nb. Bordeaux (1979-1980), exposé no18,36 pages
[17] [Iwa 2] Iwaniec, H.: Mean values for Fourier coefficients of cusp forms and sums of Kloosterman sums. Proceedings from the Journées Arithmétiques at Exeter in press (1982) · Zbl 0494.10035
[18] [Iwa 3] Iwaniec, H.: On mean values for Dirichlet’s polynomials and the Riemann zeta-function. J. London Math. Soc.22, (2), 39-45 (1980) · Zbl 0439.10026
[19] [Iwa 4] Iwaniec, H.: On the Brun-Titchmarsh theorem. J. Math. Soc. Japan34, 95-123 (1982) · Zbl 0486.10033
[20] [Kub] Kubota, T.: Elementary Theory of Eisenstein Series. New-York: John Wiley and Sons 1973 · Zbl 0268.10012
[21] [Kuz1] Kuznietsov, N.V.: Petersson hypothesis for forms of weight zero and Linnik hypothesis (in Russian), Preprint no02, Khab. KHII, Khabarovsk 1977
[22] [Kuz2] Kuznietsov, N.V.: Petersson hypothesis for parabolic forms of weight zero and Linnik hypothesis. Sums of Kloostermann sums. Math. Sbornik111, (153), no3, 334-383 (1980)
[23] [Lin] Linnik, Yu.V.: Additive problems and eigenvalues of the modular operators. Proc. Internat. Congr. Math. Stockholm 270-284 (1962)
[24] [Maa1] Maass, H.: Über eine neue Art von nichtanalytischen automorphen Funktionen. Math. Ann.121, (o2) 141-183 (1949) · Zbl 0034.31702
[25] [Maa2] Maass, H.: On modular functions of one complex variable. Tata Institute, Bombay, 1964 · Zbl 0254.10018
[26] [Mon] Montgomery, H.L.: Topics in multiplicative number theory. Lect. Notes in Math. vol. 227. Berlin-New-York: Springer 1971 · Zbl 0216.03501
[27] [Pet] Petersson, H.: Über die Entwicklungskoeffizienten der automorphen Formen. Acta Math.58, 169-215 (1932) · JFM 58.1110.01
[28] [Pro1] Proskurin, N.V.: Summation formulas for generalized Kloosterman sums (in Russian). Zap. Nau?n. Sem. Leningrad. Otdel. Mat. Inst. Steklov.82, 103-135 (1979)
[29] [Pro2] Proskurin, N.V.: On a hypothesis of Yu.V. Linnik (in Russian). Zap. Nau?n. Sem. Leningrad Otdel. Mat. Inst. Steklov.91, 94-118 (1979)
[30] [Pro3] Proskurin, N.V.: The estimations of the eigenvalues of Hecke’s operators in the space of parabolic forms of weight zero. Studies in Number Theory, vol. 5, 136-143 (1979). Pub. Math. Inst. Steklov · Zbl 0425.10028
[31] [Ran] Rankin, R.: Modular forms and functions. Cambridge-London-New-York: Cambridge University Press 1977 · Zbl 0376.10020
[32] [Roe1] Roelcke, W.: Über die Wellengleichung bei Grenzkreisgruppen erster Art. Sitz. Ber. Heidl. Akad. der Wiss. (Math. natur. Kl.) 1956, 4. Abh.
[33] [Roe2] Roelcke, W.: Das Eigenwertproblem der automorphen Formen in der hyperbolischen Ebene. I. II. Math. Ann.167, 292-337 (1966);168, 261-324 (1967) · Zbl 0152.07705
[34] [Sel1] Selberg, A.: Harmonic analysis and discontinuous groups in weakly symmetric Riemannian spaces with applications to Dirichlet’s series. J. Indian Mat. Soc.20, 47-87 (1956) · Zbl 0072.08201
[35] [Sel2] Selberg, A.: On the estimation of Fourier coefficients of modular forms. Proc. Symposia in Pure Math. VIII, A.M.S., Providence 1965, pp. 1-15
[36] [Shi] Shimura, G.: Introduction to the arithmetic theory of automorphic functions. Princeton: Princeton University Press 1971 · Zbl 0221.10029
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