Mahler, K. Fifty years as a Mathematician. (English) Zbl 0482.10002 J. Number Theory 14, 121-155 (1982). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 2 ReviewsCited in 7 Documents MSC: 11-03 History of number theory 01A70 Biographies, obituaries, personalia, bibliographies 11Hxx Geometry of numbers 11Jxx Diophantine approximation, transcendental number theory Keywords:biography; list of publications PDF BibTeX XML Cite \textit{K. Mahler}, J. Number Theory 14, 121--155 (1982; Zbl 0482.10002) Full Text: DOI OpenURL Online Encyclopedia of Integer Sequences: Decimal expansion of Pi*BesselY(0,2)/(2*BesselJ(0,2)) - gamma, where BesselJ and BesselY are the Bessel functions of the first and second kind, respectively, and gamma is Euler’s constant (A001620). References: [1] Baker, A, () [2] Cassels, J.W.S, () [3] Gelfond, O.A, (), [Russian] [4] {\scHensel, K.} Zahlentheorie (1913), Göschensche Verlagbuchhandlung, Leipzig. 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London math. soc., 18, 201-210, (1943) · Zbl 0060.12003 [34] Mordell, L.J, The minimum of a binary cubic form, II, J. London math. soc., 18, 210-217, (1943) · Zbl 0060.12003 [35] Mordell, L.J, On the geometry of numbers in some non-convex regions, (), 339-390 · Zbl 0060.11805 [36] Remak, R, Vereinfachung eines blichfeldtschen beweises aus der geometrie der zahlen, Math. Z., 26, 694-699, (1927) · JFM 53.0166.02 [37] Roth, K.F, Rational approximations to algebraic numbers, Mathematika, 2, 1-20, (1955) · Zbl 0064.28501 [38] Schmidt, W.M, T-numbers do exist, (), 1970 · Zbl 0223.10018 [39] Schmidt, W.M, Simultaneous approximations to algebraic numbers by rationals, Acta math., 125, 189-201, (1970) · Zbl 0205.06702 [40] Schneider, Th, Transzendenzuntersuchungen periodischer funktionen, I, J. reine angew. math., 172, 65-69, (1934) · Zbl 0010.10501 [41] Schneider, Th, Transzendenzuntersuchungen periodischer funktionen, II, J. reine angew. math., 172, 70-74, (1934) · Zbl 0010.10601 [42] Schneider, Th, Über die approximation algebraischer zahlen, J. reine angew. math., 175, 182-192, (1936) · JFM 62.0185.02 [43] Shidlovski, A.B, On a criterion for the algebraic independence of the values of a class of integral functions, I.a.n., 23, 35-66, (1959), [Russian] · Zbl 0085.27301 [44] Shidlovski, A.B, On the transcendency and algebraic independence of some E-functions, I.a.n., 26, 877-910, (1962), [Russian] · Zbl 0116.03906 [45] Siegel, C.L; Siegel, C.L, Approximation algebraischer zahlen, Math. Z., Ges. abh., I, No. 2, 6-46, (1921) · JFM 48.0163.07 [46] Siegel, C.L; Siegel, C.L, Über einige anwendungen diophantischer approximationen, Abh. preuss. akad. wiss., Ges. abh., I, No. 16, 209-266, (1929) · Zbl 0159.38101 [47] Siegel, C.L; Siegel, C.L, Über gitterpunkte in konvexen Körpern und ein damit zusammenhängendes extremalproblem, Acta math., Ges. abh., I, No. 19, 311-325, (1935) · Zbl 0012.39502 [48] Siegel, C.L; Siegel, C.L, A Mean value theorem in the geometry of numbers, Ann. of math., Ges. abh., III, No. 50, 39-46, (1945) [49] Thue, A, Om en generel i store Hele tal ulösbar ligning, Norske vid. selsk. skr., 7, (1908) · JFM 40.0256.01 [50] Thue, A, Über annäherungswerte algebraischer zahlen, J. reine angew. math., 135, 284-305, (1909) · JFM 40.0265.01 [51] Weyl, H, On the geometry of numbers, (), 268-289 · Zbl 0028.34902 [52] On the translation properties of a simple class of arithmetical functions, J. math. phys., 6, 158-163, (1927) · JFM 53.0265.03 [53] Über die nullstellen der unvollständigen gammafunktionen, Dr. dissertation Frankfurt, Palermo rend., 54, (1930), printed in [54] Über einen satz von Mellin, Math. ann., 100, 384-398, (1928) · JFM 54.0369.03 [55] Arithmetische eigenschaftern der Lösungen einer klasse von funktionalgleichungen, Math. ann., 101, 342-366, (1929), Papers which are related to the matter discussed in these notes [56] Uber die nullstellen der abschnitte der hypergeometrischen reihe, Math. ann., 101, 267-274, (1929) [57] Zur fortsetzbarkeit gewisser dirichletscher reihen, Math. ann., 102, 30-48, (1929) · JFM 55.0201.03 [58] Über das verschwinden von potenzreihen mehrerer veränderlichen in gewissen punktfolgen, Math. ann., 103, 573-587, (1930), Papers which are related to the matter discussed in these notes · JFM 56.0185.03 [59] Arithmetische eigenschaften einer klasse transzendental-transzendenter funktionen, Math. Z., 32, 545-585, (1930), Papers which are related to the matter discussed in these notes · JFM 56.0186.01 [60] Über beziehungen zwischen der zahl e und liouvilleschen zahlen, Math. Z., 31, 729-732, (1930), Papers which are related to the matter discussed in these notes · JFM 56.0188.01 [61] Ein beweis der thue-siegelschen satzes über die approximation algebraischer zahlen für binomische gleichungen, Math. ann., 105, 267-276, (1931), Papers which are related to the matter discussed in these notes · JFM 57.0242.02 [62] Zur approximation der exponentialfunktion und des logarithmus, I, J. reine angew. math., 166, 118-136, (1931), Papers which are related to the matter discussed in these notes [63] Über das mass der menge aller S-zahlen, Math. ann., 106, 131-139, (1932), Papers which are related to the matter discussed in these notes · JFM 58.0206.04 [64] Zur approximation der exponentialfunktion und des logarithmus, II, J. reine angew. math., 166, 137-150, (1932), Papers which are related to the matter discussed in these notes [65] Ein beweis der transzendenz der P-adischen exponentialfunktion, J. reine angew. math., 169, 61-66, (1932), Papers which are related to the matter discussed in these notes [66] Einige satze über diophantische approximationen, Jber. deutsche math. ver., (1932), 74-76 cursiv. Papers which are related to the matter discussed in these notes · JFM 58.1041.02 [67] Über die darstellung von zahlen durch binärformen höheren grades, (), Papers which are related to the matter discussed in these notes · JFM 58.1033.05 [68] Zur approximation algebraischer zahlen, I, Math. ann., 107, 691-730, (1933), Papers which are related to the matter discussed in these notes [69] Zur approximation algebraischer zahlen, II, Math. ann., 108, 37-55, (1933), Papers which are related to the matter discussed in these notes [70] Zur approximation algebraischer zahlen, III, Acta math., 62, 91-166, (1933), Papers which are related to the matter discussed in these notes [71] Über den grössten primteiler der polynome x2 ± 1, Archiv math. og. naturv., 41, (1933) [72] Über die rationalen punkte auf kurven vom geschlecht I, J. reine angew. math., 170, 168-178, (1933), Papers which are related to the matter discussed in these notes · Zbl 0008.20002 [73] Zur approximation P-adischer irrationalzahlen, Nieuw arch. wisk., 22-34, (1934) · Zbl 0009.20003 [74] Über die darstellungen einer zahl als summe von drei biquadraten, Mathematica (zutphen), 3, (1934) · Zbl 0009.29803 [75] Über die approximation P-adischer zahlen, Jber. deutsche math. ver., 250-255, (1934), Papers which are related to the matter discussed in these notes [76] Eine arithmetische eigenschaft der recurrierenden reihen, Mathematica (zutphen), 3, (1935) [77] On Hecke’s theorem on the real zeros of the L-function and the class number of quadratic fields, J. London math. soc., 9, 298-302, (1935) [78] Über eine klasseneinteilung der transzendenten zahlen, Mathematica (zutphen), 3B, (1935), Papers which are related to the matter discussed in these notes [79] (), 431-466, Papers which are related to the matter discussed in these notes [80] On the division values of Weierstrass’s p-function, Quart. J. Oxford ser., 6, 74-77, (1935) · Zbl 0011.11704 [81] Über transzendente p-adische zahlen, Compositio math., 2, 259-275, (1935), Papers which are related to the matter discussed in these notes · Zbl 0012.05302 [82] Über die taylorkoeffizienten rationaler funktionen, Akad. Amsterdam, 38, 51-60, (1935) [83] Über den grössten primteiler spezieller polynome 2. grades, Arch. math. og naturv., 41, 3-26, (1935) [84] Ein neues prinzip für transzendenzbeweise, Akad. Amsterdam, 38, 864-871, (1935), Papers which are related to the matter discussed in these notes · JFM 61.0187.02 [85] Über pseudobewertungen, I, Acta math., 66, 79-119, (1935) [86] Eine arithmetische eigenschaft der kubischen formen, Nieuw arch. wisk., (1936) [87] Über polygone mit in- oder umkreis, Mathematica (zutphen), 4A, (1936) [88] Über pseudobewertungen, II, Acta math., 67, 51-80, (1936) [89] Über pseudobewertungen, III, Acta math., 67, 283-328, (1936) · Zbl 0016.00504 [90] Über pseudobewertungen, ia, Akad. Amsterdam, 39, 57-65, (1936) · Zbl 0013.14703 [91] Note on hypothesis K of Hardy and Littlewood, J. London math. soc., 11, 136-138, (1936) [92] Ein analog zu einem schneiderschen satz, I, Akad. Amsterdam, 39, 663, (1936), Papers which are related to the matter discussed in these notes [93] Ein analog zu einem schneiderschen satz, II, Akad. Amsterdam, 39, 729-737, (1936), Papers which are related to the matter discussed in these notes [94] Über die annäherung algebraischer zahlen durch periodische algorithmen, Acta math., 68, 109-144, (1937), Papers which are related to the matter discussed in these notes [95] Neuer beweis eines satzes von A. Khintchine, Mat. sb., 43, 1, 962-963, (1937) [96] Über die dezimalbruchentwicklung gewisser irrationalzahlen, Mathematica (zutphen), 4B, (1937), Papers which are related to the matter discussed in these notes [97] Arithmetische eigenschaften ener klasse von dezimalbrüchen, Akad. Amsterdam, 40, 421-428, (1937), Papers which are related to the matter discussed in these notes [98] On the number of integers which can be represented by a binary form, J. London math. soc., 13, 134-139, (1938), Papers which are related to the matter discussed in these notes · JFM 64.0116.01 [99] On a special class of Diophantine equations, I, J. London math. soc., 13, 169-173, (1938) [100] On a special class of Diophantine equations, II, J. London math. soc., 13, 173-177, (1938) [101] Ein p-adisches analog zu einem satz von Tchebycheff, Mathematida (zutphen), 7B, (1938) [102] On the fractional parts of the powers of a rational number, Acta arith., 3, 89-93, (1938), Papers which are related to the matter discussed in these notes [103] Über einen satz von th. Schneider, Acta arith., 3, 94-101, (1938), Papers which are related to the matter discussed in these notes · JFM 64.0152.01 [104] A theorem on inhomogeneous Diophantine inequalities, Akad. Amsterdam, 41, 634-637, (1938), Papers which are related to the matter discussed in these notes · JFM 64.0147.01 [105] Eine bemerkung zum beweis der eulerschen summenformel, Mathematica (zutphen), 7B, (1938) · Zbl 0019.40303 [106] On Minkowski’s theory of the reduction of positive definite quadratic forms, Quart. J., 9, 259-262, (1938), Papers which are related to the matter discussed in these notes · JFM 64.0105.02 [107] Ein übertragungsprinzip für linearformen, Časopis, 68, 85-92, (1939), Papers which are related to the matter discussed in these notes [108] Ein übertragungsprinzip für konvexe Körper, Časopis, 68, 93-102, (1939), Papers which are related to the matter discussed in these notes [109] Some arithmetical properties of the convergents of a continued fraction, J. London math. soc., 14, 12-18, (1939), (with P. Erdös) · Zbl 0020.29403 [110] Über polare konvexe Körper, Mathematica (zutphen), 7B, (1939) [111] On the solutions of algebraic differential equations, Akad. Amsterdam, 42, 61-63, (1939) [112] A proof of Hurwitz’s theorem, Mathematica (zutphen), 8B, (1939) · JFM 65.0173.02 [113] Bemerkungen über die diophantischen eigenschaften der reellen zahlen, Mathematica (zutphen), 8B, 11-16, (1939) [114] On the minimum of positive definite Hermitian forms, J. London math. soc., 14, 137-143, (1939) · JFM 65.0174.02 [115] On a geometric representation of p-adic integers, Ann. of math., 41, 8-56, (1940) [116] On the product of two complex linear polynomials in two variables, J. London math. soc., 15, 213-236, (1940) · Zbl 0027.15802 [117] Note on the sequence √n (mod 1), Nieuw arch. wisk., 20, 176-178, (1940) [118] On the exceptional points on cubic curves, J. London math. soc., 15, 32-43, (1940), (with G. Billing) [119] On a special functional equation, J. London math. soc., 15, 115-123, (1940) [120] Über polynome mit ganzen rationalen koeffizienten, Mathematica (zutphen), 8B, 173-182, (1940) · Zbl 0022.30104 [121] On reduced positive definite ternary quadratic forms, J. London math. soc., 15, 193-195, (1940) [122] On a property of positive definite ternary quadratic forms, J. London math. soc., 15, 305-320, (1940) · JFM 66.0185.03 [123] A analogue to Minkowski’s geometry of numbers in a field of series, Ann. of math., 42, 488-522, (1941), Papers which are related to the matter discussed in these notes · JFM 67.0140.01 [124] (), 123-133 [125] Remarks on ternary Diophantine equations, Amer. math. monthly, 49, 472-479, (1942) [126] Note on lattice points in star domains, J. London math. soc., 17, 130-133, (1942), Papers which are related to the matter discussed in these notes · Zbl 0028.11203 [127] On lattice points in an infinite star domain, J. London math. soc., 18, 233-248, (1943), Papers which are related to the matter discussed in these notes [128] (), 435-466 [129] On the densest packing of circles, Amer. math. monthly, 51, 261-270, (1944), (with B. Segre) [130] On a theorem of Minkowski on lattice points in non-convex bodies, J. London math. soc., 19, 201-205, (1944), Papers which are related to the matter discussed in these notes · Zbl 0060.11811 [131] (), 107-116, Papers which are related to the matter discussed in these notes [132] (), 116-120, Papers which are related to the matter discussed in these notes [133] On a theorem of B. Segre, Duke math. J., 12, 367-371, (1945), Papers which are related to the matter discussed in these notes [134] (), 128-157, Papers which are related to the matter discussed in these notes [135] (), 158-167, Papers which are related to the matter discussed in these notes [136] (), 168-183, Papers which are related to the matter discussed in these notes [137] On lattice points in a cylinder, Quart. J., 17, 15-18, (1946), Papers which are related to the matter discussed in these notes [138] (), 151-187, Papers which are related to the matter discussed in these notes [139] (), 622-633, Papers which are related to the matter discussed in these notes [140] Simultaneous Diophantine approximation, Duke math. J., 13, 105-111, (1946), Papers which are related to the matter discussed in these notes [141] Lattice points in star bodies, Rev. univ. nac. tacuman, 5, 113-124, (1946), Papers which are related to the matter discussed in these notes [142] On the theorem of Minkowski-Hlawka, Duke math. J., 13, 611-621, (1946), Papers which are related to the matter discussed in these notes · Zbl 0060.11810 [143] On reduced positive definite quarternary quadratic forms, Nieuw arch. wisk., 22, 207-212, (1946) [144] A remark on the continued fractions of conjugate algebraic numbers, Simon stevin, 25, 45-48, (1947) · Zbl 0030.02103 [145] (), 98-107, Papers which are related to the matter discussed in these notes [146] (), 108-118, Papers which are related to the matter discussed in these notes [147] On the generating function of integers with a missing digit, K’o Hsüeh (science), 29, 265-267, (1947), [Chinese] [148] On the adjoint of a positive definite ternary quadratic form, Sci. rec. academia sinica, 2, 21-31, (1947) [149] (), 692-703, Papers which are related to the matter discussed in these notes [150] On the minimum of a pair of positive definite Hermitean forms, Nieuw arch. wisk., 22, 324-354, (1948), Papers which are related to the matter discussed in these notes [151] On the admissible lattices of automorphic star bodies, Sci. rec. academia sinica, 2, 146-148, (1948), Papers which are related to the matter discussed in these notes [152] (), 482-485, Papers which are related to the matter discussed in these notes [153] Sui determinate minimi delle sezione di un corpo convesso, Atti accad. naz. lincei cl. sci. fis. mat. nutur., 5, 8, 251-252, (1948), Papers which are related to the matter discussed in these notes [154] On the successive minima of a bounded star domain, Ann. mat. pura appl., 27, 4, 153-163, (1948), Papers which are related to the matter discussed in these notes [155] On the critical lattices of arbitrary point sets, Canad. J. math., 1, 78-87, (1949), Papers which are related to the matter discussed in these notes [156] (), 633-642, Papers which are related to the matter discussed in these notes [157] On the theorem of Liouville in fields of positive characteristic, Canad. J. math., 1, 397-400, (1949), Papers which are related to the matter discussed in these notes · Zbl 0033.35203 [158] (), 1175-1184, Papers which are related to the matter discussed in these notes [159] On lattice points in a convex decagon, Acta math., 81, 319-351, (1949), Papers which are related to the matter discussed in these notes · Zbl 0034.02607 [160] On the continued fractions of quadratic and cubic irrationals, Ann. mat. pura appl., 30, 4, 147-172, (1949), Papers which are related to the matter discussed in these notes [161] On the arithmetic on algebraic curves, (), 28-32 [162] On algebraic relations between two units of an algebraic field, (), 47-56 [163] On a theorem of Dyson, Mat. sb., 26, 457-462, (1950), [Russian] Papers which are related to the matter discussed in these notes [164] Geometry of numbers, (), Papers which are related to the matter discussed in these notes [165] Farey sections in k(i) and k(p), Trans. roy. soc. A, 243, 585-626, (1951), (with J. W. S. Cassels and W. Ledermann) [166] On the generating function of the integers with a missing digit, J. Indian math. soc., 15A, 34-40, (1951), (translation of (96)) [167] On a question in elementary geometry, Simon stevin, 28, 90-97, (1951) [168] On the lattice determinant of two particular point sets, J. London math. soc., 28, 229-232, (1953), Papers which are related to the matter discussed in these notes [169] On the approximation of logarithms of algebraic numbers, Trans. roy. soc. A, 245, 371-398, (1953), Papers which are related to the matter discussed in these notes · Zbl 0052.04404 [170] (), 30-42, Papers which are related to the matter discussed in these notes [171] Over een maximumprobleem uit de rekenkunde, Nieuw arch. wisk., 1, 3, 1-15, (1953), (with J. Popken) [172] On the greatest prime factor of axm + byn, Nieuw arch. wisk., 1, 3, 113-122, (1953), Papers which are related to the matter discussed in these notes [173] On the composition of pseudo-valuations, Nieuw arch. wisk. (3), 1, 161-198, (1953), (with P. Cohn) [174] A problem in elementary geometry, Math. gaz., 37, 241-243, (1954) · Zbl 0056.38703 [175] On a problem in the geometry of numbers, Rendi. mat. appl. (5), 13, 1-4, (1954), Papers which are related to the matter discussed in these notes [176] On a problem in Diophantine approximations, Arch. math., 6, 208-214, (1955) · Zbl 0064.04402 [177] (), 358-379, Papers which are related to the matter discussed in these notes [178] (), 380-384, Papers which are related to the matter discussed in these notes [179] (), 385-391, Papers which are related to the matter discussed in these notes [180] On the minima of compound quadratic forms, Czech. math. J. (5), 80, 180-193, (1955), Papers which are related to the matter discussed in these notes · Zbl 0067.02305 [181] A remark on Siegel’s theorem on algebraic curves, Mathematika, 2, 116-127, (1955), Papers which are related to the matter discussed in these notes · Zbl 0066.39701 [182] (), 39-48, Papers which are related to the matter discussed in these notes [183] (), 223-238, Papers which are related to the matter discussed in these notes [184] A property of the star domain |xy| ≤ 1, Mathematika, 3, 80, (1956), Papers which are related to the matter discussed in these notes · Zbl 0074.03701 [185] Über die konvexen Körper, die sich einem sternkörper einbeschreiben lassen, Math. Z., 66, 25-33, (1956), Papers which are related to the matter discussed in these notes [186] On the fractional parts of the powers of a rational number, II, Mathematika, 4, 122-124, (1957), Papers which are related to the matter discussed in these notes [187] (), 525-531 [188] A factorial series for the rational multiples of e, Math. gaz., 42, 13-16, (1958) · Zbl 0080.03601 [189] On the Chinese remainder theorem, Math. nachr., 18, 120-122, (1958) · Zbl 0092.00301 [190] An interpolation series for continuous functions of a p-adic variable, J. reine angew. math., 199, 23-34, (1958) [191] An arithmetic property of groups of linear transformations, Acta arith., 5, 197-203, (1959) [192] On a theorem of shidlovski, (), Papers which are related to the matter discussed in these notes [193] (), 243-253 [194] An application of Jensen’s formula to polynomials, Mathematika, 7, 98-100, (1960) · Zbl 0099.25003 [195] (), 145-154 [196] A correction to the paper “an interpolation series for continuous functions of a p-adic variable”, J. reine angew. math., 208, 70-72, (1961) · Zbl 0100.04003 [197] (), 188, Papers which are related to the matter discussed in these notes [198] On the representation of integers by binary forms, Acta arith., 6, 333-363, (1961), Papers which are related to the matter discussed in these notes [199] On some inequalities for polynomials in several variables, J. London math. soc., 37, 341-344, (1962) · Zbl 0105.06301 [200] Geometric number theory, (), 151, Papers which are related to the matter discussed in these notes [201] On two extremum properties of polynomials, Illinois J. math., 7, 681-701, (1963) · Zbl 0117.04003 [202] On the approximation of algebraic numbers by algebraic integers, J. austral. math. soc., 3, 408-434, (1963), Papers which are related to the matter discussed in these notes [203] Periodic algorithms for algebraic number fields (mimeographed lecture notes), 4th summer res. inst. of the Australian math. soc., (1964), Papers which are related to the matter discussed in these notes [204] A remark on a paper of mine on polynomials, Illinois J. math., 8, 1-4, (1964) · Zbl 0128.07101 [205] An inequality for the discriminant of a polynomial, Michigan math. J., 11, 257-262, (1964) [206] Transcendental numbers, J. austral. math. soc., 4, 393-396, (1964), Papers which are related to the matter discussed in these notes [207] An inequality for a pair of polynomials that are relatively prime, J. austral. math. soc., 4, 418-420, (1964), Papers which are related to the matter discussed in these notes · Zbl 0129.05701 [208] Inequalities for ideal bases in algebraic number fields, J. austral. math. soc., 4, 425-448, (1964), Papers which are related to the matter discussed in these notes · Zbl 0218.12004 [209] Equations in free metabelian groups, Michigan math. J., 12, 417-419, (1965), (with G. Baumschlag) [210] Arithmetic properties of lacunary power series with integral coefficients, J. austral. math. soc., 5, 56-64, (1965), Papers which are related to the matter discussed in these notes · Zbl 0148.27703 [211] A remark on recursive sequences, J. math. sci. 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B. shidlovski, Math. zametki acad. nauk SSSR, 2, 25-32, (1967), [Russian] Papers which are related to the matter discussed in these notes [218] An unsolved problem on the powers of \(32\), J. austral. math. soc., 8, 313-321, (1968) · Zbl 0155.09501 [219] Perfect systems, Compositio math., 19, 95-166, (1968), Papers which are related to the matter discussed in these notes [220] (), 149-173, Papers which are related to the matter discussed in these notes [221] Remarks on a paper by W. Schwarz, J. number theory, 1, 512-521, (1969), Papers which are related to the matter discussed in these notes [222] On algebraic differential equations satisfied by automorphic functions, J. austral. math. soc., 10, 445-450, (1969) · Zbl 0207.08302 [223] Lectures on transcendental numbers, (), 248-274, Papers which are related to the matter discussed in these notes [224] A lecture on the geometry of numbers of convex bodies, Bull. amer. math. soc., 77, 319-325, (1971), Papers which are related to the matter discussed in these notes [225] A generalization of Farey sequences, J. number theory, 3, 364-370, (1971), (with H. 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Baker on the approximation of rational powers of e, Acta arith., 27, 61-87, (1975) · Zbl 0305.10030 [245] A necessary and sufficient condition for transcendency, Math. comp., 29, 145-153, (1975) · Zbl 0296.10016 [246] On the transcendency of the solutions of a special class of functional equations, Bull. austral. math. soc., 13, 389-410, (1975) · Zbl 0316.10021 [247] On certain non-Archimedean functions analogous to complex analytic functions, Bull. austral. math. soc., 14, 23-36, (1976) · Zbl 0328.12014 [248] An addition to a note of mine, Bull. austral. math. soc., 14, 397-398, (1976) · Zbl 0319.10036 [249] A theorem on Diophantine approximations, Bull. austral. math. soc., 14, 463-465, (1976) [250] Bull. austral. math. soc., 15, 477-478, (1976), Corrigendum · Zbl 0316.10022 [251] () [252] On a class of non-linear functional equations connected with modular functions, J. austral. math. soc. ser. 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