Math 163 Mathematica Project 2 Answer

About this collection

This collection grew out of a project started by Alf van der Poorten more than a decade ago and has been completed by his family, friends, and colleagues. Specifically, this archive is here today in memory of Alf van der Poorten.

In addition to papers collected by Alf van der Poorten, works have been collected by Jon Borwein, Yann Bugeaud, and Michael Coons. This website looks so nice thanks to the efforts of January Cole. Special thanks are also due to Joy van der Poorten for her support of this project.

The Collected Works of Kurt Mahler are arranged chronologically below. You can quickly skip to a decade by using the links provided.

• 1920s
• 1930s
• 1940s
• 1950s
• 1960s
• 1970s
• 1980s
• 1990s

1920s

1927

1. On the translation properties of a simple class of arithmetical functions
(part two of: Norbert Wiener, The spectrum of an array and its application to the study of the translation properties of a simple class of arithmetical functions),
J. Math. and Physics 6, (1927), 158-163. [Jbuch 53, 205]
[Remark: Reprinted in Publ. MIT Ser. II 62 No. 118 (1927)]

2. Über die Nullstellen der unvollständigen Gammafunktionen, Dr. Dissertation Frankfurt (1927),
Rend. Circ. Mat. Palermo 54 (1930), 1-41. [Jbuch 56, 310]
[Remark: Note "Lebenslauf" at end of thesis.]

1928

3. Über einen Satz von Mellin,
Math. Ann. 100 (1928), 384-398. [Jbuch 54, 369]

1929

• 4. Arithmetische Eigenschaften der Lösungen einer Klasse von Funktionalgleichungen,
  Math. Ann. 101 (1929), 342-366. [Jbuch 55, 115; 56, 185]
  [Remark: Plus "Berichtigung", Math. Ann. 103, 532]
  


• 5. Über die Nullstellen der Abschnitte der hypergeometrischen Reihe,
  Math. Ann. 101 (1929), 367-374. [Jbuch 55, 219]
  


• 6. Zur Fortsetzbarkeit gewisser Dirichletscher Reihen,
  Math. Ann. 102 (1929), 30-48. [Jbuch 55, 201]
  

1930s

1930

• 7. Über das Verschwinden von Potenzreihen mehrerer Veränderlichen in speziellen Punktfolgen,
  Math. Ann. 103 (1930), 573-587. [Jbuch 56, 185]
  

8. Arithmetische Eigenschaften einer Klasse transzendental-transzendente Funktionen,
Math. Z. 32 (1930), 545-585. [Jbuch 55, 186]

9. Über Beziehungen zwischen der Zahl e und Liouvilleschen Zahlen,
Math. Z. 31 (1930), 729-732. [Jbuch 56, 188]

1931

10. Ein Beweis des Thue-Siegelschen Satzes über die Approximation algebraischer Zahlen für binomische Gleichungen,
10a. English translation by Karl Levy, 2015: A proof of the Thue-Siegel Theorem about the approximation of algebraic numbers for binomial equations,
Math. Ann. 105 (1931), 267-276. [Zblatt 2, 184]

11. Zur Approximation der Exponentialfunktion und des Logarithmus. Teil I,
J. Reine Angew. Math. 166 (1931), 118-136. [Zblatt 3, 151]

1932

12. Über das Mass der Menge aller S-Zahlen,
Math. Ann. 106 (1932), 131-139. [Zblatt 3, 246]

13. Zur Approximation der Exponentialfunktion und des Logarithmus. Teil II,
J. Reine Angew. Math. 166 (1932), 137-150. [Zblatt 3, 388]

14. Ein Beweis der Transzendenz der P-adischen Exponentialfunktion,
J. Reine Angew. Math. 169 (1932), 61-66. [Zblatt 6, 11]

15. Einige Sätze über Diophantische Approximationen,
Jahresbericht d. Deutschen Math. Verein. 41 (1932), 74-76.

16. Über die Darstellung von Zahlen durch Binärformen höheren Grades,
Kongressbericht, Zürich, (1932), 2pp.

1933

17. Zur Approximation algebraischer Zahlen. I. (Über den grössten Primteiler binärer Formen),
Math. Ann. 107 (1933), 691-730. [Zblatt 6, 105]

18. Zur Approximation algebraischer Zahlen. II. (Über die Anzahl der Darstellungenganzer Zahlen durch Binärformen),
Math. Ann. 108 (1933), 37-55. [Zblatt 6, 156]

19. Zur Approximation algebraischer Zahlen. III. (Über die mittlere Anzahl der Darstellungen grosser Zahlen durch binäre Formen),
Acta Math. 62 (1933), 91-166. [Zblatt 8, 198]

20. Über den grössten Primteiler der Polynome \(X^2\mp 1\),
Archiv Math. og. Naturv. 41 (1933), 1-8. [Zblatt 12, 394]

21. Über die rationalen Punkte auf Kurven vom Geschlecht Eins,
J. Reine Angew. Math. 170 (1933), 168-178. [Zblatt 8, 200]

1934

22. Zur Approximation P-adischer Irrationalzahlen,
Nieuw Arch. Wisk. 18 (1934), 22-34. [Zblatt 9, 200]

23. Über die Darstellungen einer Zahl als Summe von drei Biquadraten,
Mathematica(Zutphen) 3 (1934), 69-72. [Zblatt 9, 298]

24. Über Diophantische Approximationen in Gebiete der p-adische Zahlen,
Jahresbericht d. Deutschen Math. Verein. 44 (1934), 250-255. [Zblatt 10, 198]

25. Eine arithmetische Eigenschaft der rekurrierenden Reihen,
Mathematica (Zutphen) 3 (1934), 153-156. [Zblatt 10, 390]

1935

26. On Hecke's theorem on the real zeros of the L-functions and the class number of quadratic fields,
J. London Math. Soc. 9 (1935), 298-302. [Zblatt 10, 250]

27. Über eine Klasseneinteilung der P-adischen Zahlen,
Mathematica (Zutphen) 3B (1935), 177-185. [Zblatt 11, 58]

28. On the lattice points on curves of genus 1,
Proc. London Math. Soc. 39 (1935), 431-466. [Zblatt 12, 150]

29. On the division-values of Weierstrass's p-function,
Quart. J. Math. Oxford 6 (1935), 74-77. [Zblatt 11, 117]

30. Über transzendente P-adische Zahlen,
Compositio Math. 2 (1935), 259-275. [Zblatt 12, 53]

30a. A correction to "Über transzendente P-adische Zahlen",
Compositio Math. 8 (1949), p112. [Math. Rev. 12, 319], [RNT Q25-5]

31. Eine arithmetische Eigenschsaft der Taylor-Koeffizienten rationaler Funktionen,
Proc. Kon. Nederlandsche Akad. v. Wetenschappen 38 (1935), 50-60. [Zblatt 10, 390]

32. Über den grössten Primteiler spezieller Polynome zweiten Grades,
Archiv Math. og. Naturv. 41 (1935), nr 6, 3-26. [Zblatt 13, 389]

33. (with J. Popken) Ein neues Prinzip für Transzendenzbeweise,
Proc. Kon. Nederlandsche Akad. v. Wetenschappen 38 (1935), 864-871. [Zblatt 12, 341]

34. Über Pseudobewertungen, I,
Acta Math. 66 (1935), 79-119. [Zblatt 13, 51]

1936

35. Eine arithmetische Eigenschaft der kubischen Binärformen,
Nieuw Arch. Wisk. 18 (1936), 1-9. [Zblatt 14, 8]

36. Ueber Polygone mit Um- oder Inkreis,
Mathematica (Zutphen) 4A (1936), 33-42. [Zblatt 13, 176]

37. Über Pseudobewertungen II,
Acta Math. 67 (1936), 51-80. [Zblatt 14, 340]

38. Über Pseudobewertungen III,
Acta Math. 67 (1936), 283-328. [Zblatt 16, 5]

39. Über Pseudobewertungen Ia,
Proc. Kon. Nederlandsche Akad. v. Wetenschappn 39 (1936), 57-65. [Zblatt 13, 147]

40. Note on Hypothesis K of Hardy and Littlewood,
J. London Math. Soc. 11 (1936), 136-138. [Zblatt 13, 391]

41. Ein Analog zu einem Schneiderschen Satz, I,
Proc. Kon. Nederlandsche Akad. v. Wetenschappen 39 (1936), 633-640. [Zblatt 14, 205]

42. Ein Analog zu einem Schneiderschen Satz, II,
Proc. Kon. Nederlandsche Akad. v. Wetenschappen 39 (1936), 729-737. [Zblatt 14, 205]

42a. Pseudobewertungen,
Proc. ICM, Oslo (1936), 1p.

1937

43. Über die Annäherung algebraischer Zahlen durch periodische Algorithmen,
Acta Math. 68 (1937), 109-144. [Zblatt 17, 57]

44. Neuer Beweis eines Satzes von A. Khintchine,
Mat. Sb. I 43 (1937), 961-963. [Zblatt 16, 155]

45. Über die Dezimalbruchentwicklung gewisser Irrationalzahlen,
Mathematica (Zutphen) B6 (1937), 22-26. [Zblatt 18, 111]

46. Arithmetische Eigenschaften einer Klasse von Dezimalbrüchen,
Proc. Kon. Nederlandsche Akad. v. Wetenschappen 40 (1937), 421-428. [Zblatt 17, 56]

1938

47. (with P. Erdős) On the number of integers which can be represented by a binary form,
J. London Math. Soc. 13 (1938), 134-139. [Zblatt 18, 344]

48. On a special class of Diophantine equations, I,
J. London Math. Soc. 13 (1938), 169-173. [Zblatt 19, 250]

49. On a special class of Diophantine equations, II,
J. London Math. Soc. 13 (1938), 173-177. [Zblatt 19, 250]

50. Ein p-adisches Analogon zu einem Satz von Tchebycheff,
Mathematica (Zutphen) B7 (1938), 2-6. [Zblatt 18, 346]

51. On the fractional parts of the powers of a rational number,
Acta Arith. 3 (1938), 89-93. [Zblatt 19, 250]

52. Über einen Satz von Th. Schneider,
Acta Arith. 3 (1938), 94-101. [Zblatt 19, 250]

53. A theorem on inhomogenous Diophantine inequalities,
Proc. Kon. Nederlandsche Akad. v. Wetenschappen 41 (1938), 634-637. [Zblatt 19, 51]

54. Eine Bemerkung zum Beweis der Eulerschen Summenformel,
Mathematica (Zutphen) B7 (1938), 33-42. [Zblatt 19, 403]

55. On Minkowski's theory of reduction of positive definite quadratic forms,
Quart. J. Math. Oxford 9 (1938), 259-262. [Zblatt 19, 395]

1939

56. Ein Übertragungsprinzip für lineare Ungleichungen,
Math. Časopis 68 (1939), 85-92. [Math. Rev. 1, 202], [RNT H05-1]

57. Ein Übertragungsprinzip für konvexe Körper,
Math. Časopis 68 (1939), 93-102. [Math. Rev. 1, 202H05-2]

58. (with P. Erdös) Some arithmetical properties of the convergents of a continued fraction,
J. London Math. Soc. 14 (1939), 12-18. [Zblatt 20, 390]

59. Ein Minimal problem für convexe Polygone,
Mathematica (Zutphen) B7 (1938), 118-127. [Zblatt 20, 50]

60. On a the solutions of algebraic differential equations,
Proc. Kon. Nederlandsche Akad. v. Wetenschappen 42 (1939), 61-63. [Zblatt 21, 27]

61. A proof of Hurwitz's theorem,
Mathematica (Zutphen) 8B (1939), 57-61. [Math. Rev. 1, 39], [RNT J28-1]

62. Bemerkungen über die Diophantischen Eigenschaften der reellen Zahlen,
Mathematica (Zutphen) 8B (1939), 11-16. [Zblatt 21, 296]

63. On the minimum of positive definite Hermitian forms,
J. London Math. Soc. 14 (1939), 137-143. [Zblatt 22, 6]

1940s

1940

64. On a geometrical representation of p-adic numbers,
Ann. of Math. (2) 41 (1940), 8-56. [Math. Rev. 1, 295], [RNT J64-2]

65. On the product of two complex linear polynomials in two variables,
J. London Math. Soc. 15 (1940), 213-236. [Math. Rev. 2, 148], [RNT J56-1]
[Remark: Mahler writes "This is an extension of an earlier paper which was accepted for publication by Acta Arith. in February 1939 of which I had just received the first proofs when war broke out".]

66. Note on the sequence \(\sqrt{n}\ (\bmod\ 1)\),
Nieuw Arch. Wisk. 20 (1940), 176-178. [Math. Rev. 1, 202], [RNT J24-1]

67. (with G. Billing) On exceptional points on cubic curves,
J. London Math. Soc. 15 (1940), 32-43. [Zblatt 26, 199], [Math. Rev. 1, 266]

68. On a special functional equation,
J. London Math. Soc. 15 (1940), 115-123. [Math. Rev. 2, 133], [RNT P80-3]

69. Über Polynome mit ganzen rationalen Koeffizienten,
Mathematica (Zutphen) 8B (1940), 173-182. [Math. Rev. 2, 148], [RNT J84-2]

70. On reduced positive definite ternary quadratic forms,
J. London Math. Soc. 15 (1940), 193-195. [Zblatt 27, 151], [Math. Rev. 2, 119]

71. On a property of positive definite ternary quadratic forms,
J. London Math. Soc. 15 (1940), 305-320. [Math. Rev. 2, 25], [RNT J48-1]

1941

72. An analogue to Minkowski's Geometry of Numbers in a field of series,
Ann. of Math. (2) 42 (1941), 488-522. [Math. Rev. 2, 350], [RNT H05-4]

1942

73. On ideals in the Cayley-Dickson algebra,
Proc. Royal Irish Academy 48 (1942), 123-133. [Math. Rev. 4, 185]

74. Remarks on ternary Diophantine equations,
Amer. Math. Monthly 49 (1942), 372-378. [Math. Rev. 4, 34], [RNT N32-1]

75. Note on lattice points in star domains,
J. London Math. Soc. 17 (1942), 130-133. [Math. Rev. 4, 212], [RNT H15-2]

1943

76. On lattice points in an infinite star domain,
J. London Math. Soc. 18 (1943), 233-238. [Math. Rev. 6, 11], [RNT H20-4]

1944

77. A problem of Diophantine approximation in quaternions,
Proc. London Math. Soc. (2) 48 (1944), 435-466. [Math. Rev. 8, 137], [RNT J32-3]

78. (with B. Segre) On the densest packing of circles,
Amer. Math. Monthly 51 (1944), 261-270. [Zblatt 60, 117; 60, 349], [Math. Rev. 6, 16]

79. On a theorem of Minkowski on lattice points in non-convex point sets,
J. London Math. Soc. 19 (1944), 201-205. [Math. Rev. 7, 244], [RNT H25-3]

80. On lattice points in the domain \(|xy|\leq 1,\ |x + y|\leq 5^{1/2}\), and applications to asymptotic formulae in lattice point theory, I,
Proc. Cambridge Phil. Soc. 40 (1944), 107-116. [Math. Rev. 6, 119], [RNT H20-4]

81. On Lattice points in the domain \(|xy|\leq 1,\ |x + y|\leq 5^{1/2}\), and applications to asymptotic formulae in lattice point theory, II,
Proc. Cambridge Phil. Soc. 40 (1944), 116-120. [Math. Rev. 6, 119], [RNT H20-4]

1945

82. A theorem of B. Segre,
Duke Math. J. 12 (1945), 367-371. [Math. Rev. 6, 258], [RNT J08-2]

1946

83. Lattice points in two-dimensional star domains, I,
Proc. London Math. Soc. 49 (1946), 128-157. [Math. Rev. 8, 12], [RNT H15-6]

84. Lattice points in two-dimensional star domains, II,
Proc. London Math. Soc. 49 (1946), 158-167. [Math. Rev. 8, 195], [RNT H20-10]

85. Lattice points in two-dimensional star domains, III,
Proc. London Math. Soc. 49 (1946), 168-183. [Math. Rev. 8, 19], [RNT H20-11]

86. On lattice points in a cylinder,
Quart. J. Math. Oxford 17 (1946), 16-18. [Math. Rev. 7, 368], [RNT H10-3]

87. On lattice points in n-dimensional star bodies, I, Existence theorems,
Philos. Trans. Roy. Soc. London Ser. A 187 (1946), 151-187. [Math. Rev. 8, 195], [RNT H15-7]

88. Lattice points in n-dimensional star bodies. II. Reducibility theorems. I, II, III, IV,
Proc. Kon. Nederlandsche Akad. v. Wetenschappen 49 (1946), 331-343, 444-454, 524-532, 622-631 =
Indag. Math. 8 200-212, 299-309, 343-351, 381- 390. [Math. Rev. 8, 12], [RNT H15-8, 9]

89. (with H. Davenport) Simultaneous Diophantine approximation,
Duke Math. J. 13 (1946), 105-111. [Math. Rev. 7, 506], [RNT J12-6]

90. Lattice points in n-dimensional star bodies,
Rev. Univ. Nac. Tucumán A 5 (1946), 113-124. [Math. Rev. 8, 566], [RNT H15-10

91. The theorem of Minkowski-Hlawka,
Duke Math. J. 13 (1946), 611-621. [Math. Rev. 8, 444], [RNT H25-5]

92. On reduced positive definite quarternary quadratic forms,
Nieuw Arch. Wisk. 22 (1946), 207-212. [Math. Rev. 8, 369], [RNT J44-4]

1947

93. A remark on the continued fractions of conjugate algebraic numbers,
Simon Stevin 25 (1947), 45-48. [Math. Rev. 8, 318], [RNT A56-10]

94. On irreducible convex domains,
Proc. Kon. Nederlandsche Akad. v. Wetenschappen 50 (1947), 98-107 =
Indag. Math. 9 73-82. [Math. Rev. 8, 445], [RNT H15-13]

95. On the area and the densest packing of convex domains,
Proc. Kon. Nederlandsche Akad. v. Wetenschappen 50 (1947), 108-118 =
Indag. Math. 9 83-93. [Math. Rev. 8, 445], [RNT H15-14]

96. On the generating functions of integers with a missing digit [in Chinese],
K'o Hsüeh Science 29 (1947), 265-267. [Math. Rev. 9, 79], [RNT J76-13]

97. On the adjoint of a reduced positive definite ternary quadratic form,
Sci. Rec. Academia Sinica 2 (1947), 21-31. [Math. Rev. 9, 270], [RNT E20-18]

98. On the minimum determinant and the circumscribed hexagons of a convex domain,
Proc. Kon. Nederlandsche Akad. v. Wetenschappen 50 (1947), 692-703 =
Indag. Math. 9 326-337. [Math. Rev. 9, 10], [RNT H05-10]

1948

99. (with K.C. Hallum) On the minimum of a pair of positive definite Hermitean forms,
Nieuw Arch. Wisk. 22 (1948), 324-354. [Math. Rev. 9, 334], [RNT J28-4]

100. On the admissible lattices of automorphic star bodies,
Sci. Rec. Academia Sinica 2 (1948), 146-148. [Math. Rev. 1, 102], [RNT H15-22]

101. On lattice points in polar reciprocal convex domains,
Proc. Kon. Nederlandsche Akad. v. Wetenschappen 51 (1948), 176-179 =
Indag. Math. 10 482-485. [Math. Rev. 9, 501], [RNT H05-11]

102. Sui determinante minimi delle sezione di un corpo convesso,
Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. (8) 5 (1948), 251-252. [Math. Rev. 10, 593], [RNT H05-17]

103. On the successive minima of a bounded star domain,
Ann. Mat. Pura Appl. (4) 27 (1948), 153-163. [Math. Rev. 11, 13], [RNT H15-37]

1949

104. On the critical lattices of arbitrary point sets,
Canad. J. Math. 1 (1949), 78-87. [Math. Rev. 10, 355], [RNT H15-29]

105. On the minimum determinant of a special point set,
Proc. Kon. Nederlandsche Akad. v. Wetenschappen 52 (1949), 633-642 =
Indag. Math. 11, 195-204. [Math. Rev. 10, 512], [RNT H15-33]

106. On a theorem of Liouville in fields of positive characteristic,
Canad. J. Math. 1 (1949), 397-400. [Math. Rev. 11, 159], [RNT J68-9]

107. On Dyson's improvement of the Thue-Siegel theorem,
Proc. Kon. Nederlandsche Akad. v. Wetenschappen 52 (1949), 449-458 =
Indag. Math. 11 1175-1184. [Math. Rev. 11, 583], [RNT J68-9]

108. (with W. Ledermann) On lattice points in a convex decagon,
Acta Math. Acad. Sci. Hungar. 81 (1949), 319-351. [Math. Rev. 11, 233], [RNT H10-15]

109. On the continued fractions of quadratic and cubic irrationals,
Ann. Mat. Pura Appl. (4) 30 (1949), 147-172. [Math. Rev. 12, 245], [RNT A56-19]

110. On the arithmetic on algebraic curves,
in Seminar on Algebra and Number Theory, Chicago, (1949), 28-32.

111. On algebraic relations between two units of an algebraic field,
in "Algèbre théorie des nombres", Colloques internationaux du CNRS 24 (1949), 47-55. CNRS, Paris, 1950. [Math. Rev. 13, 202], [RNT D40-16]

1950s

1950

112. On a theorem of Dyson [in Russian],
Mat. Sb. 26 (1950), 457-462. [Math. Rev. 12, 319], [RNT J16-10]

113. Geometry of Numbers, [Lecture notes]
Lectures given at the University of Colorado in the summer of 1950, (1950).

1951

114. (with J.W.S. Cassels and W. Ledermann) Farey section in k(i) and k(ρ),
Philos. Trans. Roy. Soc. London Ser. A 243 (1951), 585-626. [Math. Rev. 13, 323], [RNT J56-13]

114a. Farey section in the fields of Gauss and Eisenstein,
Proc. International Congress Cambridge, Mass. 1950 1 (1952), 281-285. [Math. Rev. 13, 538]

115. On the generating function of the integers with a missing digit,
J. Indian Math. Soc. 15A (1951), 34-40. [Math. Rev. 13, 213], [RNT J76-14]
[Remark: Translation of (96)]

116. On a question in elementary geometry,
Simon Stevin 28 (1951), 90-97. [Math. Rev. 13, 152]

1953

117. On the lattice determinants of two particular point sets,
J. London Math. Soc. 28 (1953), 229-232. [Math. Rev. 14, 850], [RNT H20-19]

118. On the approximation of logarithms of algebraic numbers,
Philos. Trans. Roy. Soc. London Ser. A 245 (1953), 371-398. [Math. Rev. 14, 624], [RNT J80-8]

119. On the approximation of \(\pi\),
Proc. Kon. Nederlandsche Akad. v. Wetenschappen Ser. A 56 (1953), 30-42 =
Indag. Math. 15, 30-42. [Math. Rev. 14, 957], [RNT J80-9]

120. (with J. Popken) Over een Maximumprobleem uit de Rekenkunde,
Nieuw Arch. Wisk. (3) 1 (1953), 1-15. [Math. Rev. 14, 852]

121. On the greatest prime factor of \(ax^m+by^n\),
Nieuw Arch. Wisk. (3) 1 (1953), 113-122. [Math. Rev. 15, 289], [RNT N32-14]

122. (with P. M. Cohn) On the composition of pseudo-valuations,
Nieuw Arch. Wisk. (3) 1 (1953), 161-198. [Math. Rev. 15, 395]

1954

123. A problem in elementary geometry,
Math. Gaz. 37 (1954), 241-243. [Math. Rev. 16, 738]

124. On a problem in the geometry of numbers,
Rendi. Mat. Appl. (5) 14 (1954), 38-41. [Math. Rev. 16, 802], [RNT H05-38]

1955

125. On a problem in Diophantine approximations,
Archiv Math. og. Naturv. 6 (1955), 208-214. [Math. Rev. 16, 1002], [RNT J12-29]

126. On compound convex bodies, I,
Proc. London Math. Soc. (3) 5 (1955), 358-379. [Math. Rev. 17, 589], [RNT H05-46]

127. On compound convex bodies, II,
Proc. London Math. Soc. (3) 5 (1955), 380-384. [Math. Rev. 17, 589], [RNT H05-47]

128. The p-th compound of a sphere,
Proc. London Math. Soc. (3) 5 (1955), 385-391. [Math. Rev. 17, 402], [RNT H05-49]

129. On the minima of compound quadratic forms,
Czech. Math. J. (5) 80 (1955), 180-193. [Math. Rev. 17, 589], [RNT H05-48]

130. A remark on Siegel's theorem on algebraic curves,
Mathematika 2 (1955), 116-127. [Math. Rev. 18, 565], [RNT D40-27]

1956

131. On the Taylor coefficients of rational functions,
Proc. Cambridge Phil. Soc. 52 (1956), 39-48. [Math. Rev. 17, 597], [RNT Q05-25]

131a. Addendum to "On the Taylor coefficients of rational functions",
Proc. Cambridge Phil. Soc. 53 (1957), p544. [Math. Rev. 19, 691], [RNT Q05-26]

132. Invariant matrices and the geometry of numbers,
Proc. Roy. Soc. Edinburgh A 64 (1956), 223-238. [Math. Rev. 18, 196], [RNT H05-50]

133. A property of the star domain \(|xy|\leq 1\),
Mathematika 3 (1956), p80. [Math. Rev. 18, 21], [RNT H20-21]Kurt Mahler 1903-1988 21

1957

134. Über die konvexen Körper, die sich einem Sternkörper einbeschreiben lassen,
Math. Z. 66 (1957), 25-33. [ Math. Rev. 18, 668 ]

135. On the fractional parts of the powers of a rational number, II,
Mathematika 4 (1957), 122-124. [Math. Rev. 20#3], [RNT J68-19]

136. A matrix representation of the primitive residue classes \((\bmod\ 2n)\),
Proc. Amer. Math. Soc. 8 (1957), 525-531. [Math. Rev. 19, 388], [RNT A06-10]

1958

137. A factorial series for the rational multiples of e,
Math. Gaz. 42 (1958), 13-16. [Math. Rev. 20#3094], [RNT A68-15]

138. On the Chinese remainder theorem,
Math. Nachr. 18 (1958), 120-122. [Math. Rev. 20#3048], [RNT Z15-38]

139. An interpolation series for continuous functions of a p-adic variable,
J. Reine Angew. Math. 199 (1958), 23-34. [Math. Rev. 20#], [RNT Q25-11]

1959

140. An arithmetic property of groups of linear transformations,
Acta Arith. 5 (1959), 197-203. [Math. Rev. 21#6361], [RNT J28-20]

141. On a theorem of Shidlovski,
Lectures given at the Math. Centrum, Amsterdam, December 1959, (1959).

1960s

1960

142. On a theorem by E. Bombieri,
Proc. Kon. Nederlandsche Akad. v. Wetenschappen Ser. A 63 (1960), 245-253 =
Indag. Math. 22 245-253. [Math. Rev. 22#4705], [RNT J68-24]

142a. Correction to the paper "On a theorem by E. Bombieri",
Proc. Kon. Nederlandsche Akad. v. Wetenschappen Ser. A 64 (1960) 141 =
Indag. Math. 23 141. [Math. Rev. 23#A885], [RNT J68-25]

143. An application of Jensen's formula to polynomials,
Mathematika 7 (1960), 98-100. [Math. Rev. 23#A1779], [RNT J76-38]

1961

144. On the zeros of the derivative of a polynomial,
Proc. Roy. Soc. London Ser. A 264 (1961), 145-154. [Math. Rev. 24#A3271]

145. A correction the the paper "An interpolation series for continuous functions of a p-adic variable",
[Seq. No. 139], J. Reine Angew. Math. 208 (1961), 70-72. [Math. Rev. 25#3035], [RNT Q25-12]

146. Lectures on Diophantine Approximations I : g-adic Numbers and Roth's Theorem, [Lecture notes]
Lectures given at the University of Notre Dame in 1957, University of Notre Dame Press, Notre Dame,
Indiana, 188 pages, (1961). [Math. Rev. 26#78], [RNT J02-14]

147. (with D.J. Lewis) On the representation of integers by binary forms,
Acta Arith. 6 (1961), 333-363. [Math. Rev. 22#10952], [RNT D40-35]

1962

148. On some inequalities for polynomials in several variables,
J. London Math. Soc. 37 (1962), 341-344. [Math. Rev. 25#2036], [RNT J76-40]

149. Geometric number theory, [Lecture notes]
Lectures given at the University of Notre Dame in 1962, 151 pp, (1962).

1963

150. On two extremum properties of polynomials
Illinois J. Math. 7 (1963), 681-701. [Math. Rev. 28#192]

151. On the approximation of algebraic numbers by algebraic integers,
J. Austral. Math. Soc. 3 (1963), 408-434. [Math. Rev. 29#1182], [RNT J68-43]

1964

152. Periodic algorithms for algebraic number fields, [Mimeographed lecture notes]
4th Summer Research Institute of the Austral. Math. Soc. University of Sydney, January 1964 (1964), 19pp.

153. A remark on a paper of mine on polynomials,
Illinois J. Math. 8 (1964), 1-4. [Math. Rev. 28#2194]

154. An inequality for the discriminant of a polynomial,
Michigan Math. J. 11 (1964), 257-262. [Math. Rev. 29#3465], [RNT C05-29]

155. Transcendental numbers,
J. Austral. Math. Soc. 4 (1964), 393-396. [Math. Rev. 30#4727], [RNT J02-17]

156. An inequality for a pair of polynomials that are relatively prime,
J. Austral. Math. Soc. 4 (1964), 418-420. [Math. Rev. 30#3193], [RNT C05-33]

157. Inequalities for ideal bases in algebraic number fields,
J. Austral. Math. Soc. 4 (1964), 425-448. [Math. Rev. 31#1243], [RNT R24-33]

1965

158. (with G. Baumschlag) Equations in free metabelian groups,
Michigan Math. J. 12 (1965), 417-419. [Math. Rev. 31#5892]

159. Arithmetic properties of lacunary power series with integral coefficients,
J. Austral. Math. Soc. 5 (1965), 56-64. [Math. Rev. 32#7508], [RNT J76-53]

1966

160. A remark on recursive sequences,
J. Math. Sci. Delhi 1 (1966), 12-17. [Math. Rev. 35#2853], [RNT B40-52]

161. Transcendental numbers,
Encyclopaedia Brittannica, (1966), 1 column.

162. A remark on Kronecker's theorem,
Enseign Math. 12 (1966), 183-189. [Math. Rev. 35#1550], [RNT J20-39]

1967

163. (with G. Szekeres) On the approximation of real numbers by roots of integers,
Acta Arith. 12 (1967), 315-320. [Math. Rev. 35#130]

164. Applications of some formulae by Hermite to the approximation of exponentials and logarithms,
Math. Ann. 168 (1967), 200-227. [Math. Rev. 34#5754], [RNT J80-20]

165. On a class of entire functions,
Acta Math. Acad. Sci. Hungar. 18 (1967), 83-96. [Math. Rev. 34#5760], [RNT Q05-63]

166. On a lemma by A. B. Shidlovski [in Russian],
Math. Zametki Acad. Nauk SSR2 (1967), 25-32. [Math. Rev. 36#2561], [RNT J88-34]

1968

167. An unsolved problem on the powers of 3/2,
J. Austral. Math. Soc. 8 (1968), 313-321. [Math. Rev. 37#2694], [RNT K25-29]

168. Perfect systems,
Compositio Math. 19 (1968), 95-166. [Math. Rev. 39#458], [RNT J76-64]
[Remark: First publication of a manuscript written in the 30s.]

169. Applications of a theorem by A. B. Shidlovski,
Philos. Trans. Roy. Soc. London Ser. A 305 (1968), 149-173. [Math. Rev. 37#1322], [RNT J88-37]

1969

170. Remarks on a paper by W. Schwarz,
J. Number Theory 1 (1969), 512-521. [Math. Rev. 40#2611], [RNT J76-65]

171. On algebraic differential equations satisfied by automorphic functions,
J. Austral. Math. Soc. 10 (1969), 445-450. [Math. Rev. 41#7099]

172. Lectures on transcendental numbers (Summer Institute on Number Theory at Stony Brook, 1969),
Proc. Symp. Pure Math.(Amer. Math. Soc.) XX (1969), 248-274. [Math. Rev. 47#6620], [RNT I02-200]

1970s

1971

173. A lecture on the geometry of numbers of convex bodies,
Bull. Amer. Math. Soc. 77 (1971), 319-325. [Math. Rev. 43#1926], [RNT H05-89]

174. (with H. Brown) A generalization of Farey sequences: Some exploration via the computer,
J. Number Theory 3 (1971), 364-370. [Math. Rev. 44#3959], [RNT B56-14]

175. On formal power series as integrals of algebraic differential equations,
Rend. Accad. Naz. dei Lincei (8) 50 (1971), 36-49. [Math. Rev. 45#8649]

176. A remark on algebraic differential equations,
Rend. Accad. Naz. dei Lincei (8) 50 (1971), 174-184. [Math. Rev. 47#3358]

177. An arithmetical remark on entire periodic functions,
Bull. Austral. Math. Soc. 5 (1971), 191-195. [Math. Rev. 45#5361]

178. An elementary existence theorem for entire functions,
Bull. Austral. Math. Soc. 5 (1971), 415-419. [Math. Rev. 45#515]

179. On the order function of a transcendental number,
Acta Arith. 18 (1971), 63-76. [Math. Rev. 45#5090], [RNT I30-203.]

180. Transcendental numbers. I. Existence and chief characteristics of transcendental numbers [in Hungarian],
Mat. Lapok 22 (1971), 31-50. [Math. Rev. 58#27822], [RNT I20-224.]

1972

181. Transcendental numbers. II. Convergence of Laurent series and formal Laurent series [in Hungarian],
Mat. Lapok 23 (1972), 13-23. [Math. Rev. 58#27823], [RNT I20-224E]

182. On the coefficients of the \(2^n\)-th transformation polynomial for \(j(\omega)\),
Acta Arith. 21 (1972), 89-97. [Math. Rev. 46#5251], [RNT C10-206]

182a. Obituary, L. J. Mordell,
J. Number Theory 4 (1972), iii-iv. [Math. Rev.45#5068], [RNT Z20-58G]

Lectures on the reading of mathematics in Chinese,
Lecture notes, Ohio State University, 63 pages, 1972.

1973

183. The classification of transcendental numbers,
Proc. Symp. Pure Math. (Amer. Math. Soc.) XXIV (1973), 175-179. [Math. Rev. 49#2575], [RNT I30-204]

184. Introduction to p-adic Numbers and their Functions, [Book]
Cambridge Tracts in Mathematics 64, Cambridge University Press, London/New York, (1973). [Math. Rev. 50#213], [RNT S02-201]

185. Arithmetical problems of the digits of the multiples of an irrational number,
Bull. Austral. Math. Soc. 8 (1973), 191-203. [Math. Rev. 47#8448], [RNT K15- 204]

186. On a class of Diophantine inequalities,
Bull. Austral. Math. Soc. 8 (1973), 247-259. [Math. Rev. 47#8443], [RNT J20-202]

187. A p-adic analogue of a theorem by J. Popken,
J. Austral. Math. Soc. 16 (1973), 176-184. [Math. Rev. 49#2578], [RNT I25-203]

1974

188. On the coefficients of the transformation polynomials for the modular function,
Bull. Austral. Math. Soc. 10 (1974), 197-218. [Math. Rev. 50#7034], [RNT F05-219]

189. On rational approximations of the exponential function at rational points,
Bull. Austral. Math. Soc. 10 (1974), 325-335. [Math. Rev. 50#244], [RNT I25-204]

190. Polar analogues of two theorems by Minkowski,
Bull. Austral. Math. Soc. 11 (1974), 121-129. [Math. Rev. 50#7039], [RNT H25-202]

191. On the digits of the multiples of an irrational p-adic number,
Proc. Cambridge Phil. Soc. 76 (1974), 417-422. [Math. Rev. 50#221], [RNT K15-206]

192. How I became a mathematician,
Amer. Math. Monthly 81 (1974), 981-983. [Math. Rev. 50#1820], [RNT Z20-205]

1975

193. On a paper by A. Baker on the approximation of rational powers of e,
Acta Arith. 27 (1975), 61-87. [Math. Rev. 51#3070], [RNT I25-211]

194. A necessary and sufficient condition for transcendency,
Math. Comp. 29 (1975), 145-153. [Math. Rev. 52#3072], [RNT I25-214]

195. On the transcendency of the solutions of a special class of functional equations,
Bull. Austral. Math. Soc. 13 (1975), 389-410. [Math. Rev. 53#2850], [RNT I65-205]

1976

196. On certain non-archimedean functions analogous to complex analytic functions,
Bull. Austral. Math. Soc. 14 (1976), 23-36. [Math. Rev. 53#8025], [RNT Q25-225]

197. An addition to a note of mine ([190]),
Bull. Austral. Math. Soc. 14 (1976), 397-398. [Math. Rev. 54#2596], [RNT H25-202E]

198. A theorem on Diophantine approximations,
Bull. Austral. Math. Soc. 14 (1976), 463-465. [Math. Rev. 54#12667], [RNT J04-209]

199. Corrigendum to "On the transcendency of the solutions of a special class of functional equations",
Bull. Austral. Math. Soc. 15 (1976), 477-478. [Math. Rev. 54#12674]

200. Lectures on Transcendental Numbers, [Book]
B. Divis and W. J. LeVeque, eds., Lecture Notes in Mathematics 546, Springer-Verlag, Berlin/New York, (1976). [Math. Rev. 58#1077], [RNT I02-200E]

201. On a class of non-linear functional equations connected with modular functions,
J. Austral. Math. Soc. Ser. A 22 (1976), 65-118. [Math. Rev. 56#258], [RNT F10-229]

202. On a class of transcendental decimal fractions,
Comm. Pure Appl. Math. 29 (1976), 717-725. [Math. Rev. 54#12675], [RNT I30-214]

1977

203. On some special decimal fractions,
In Hans Zassenhaus ed., Number Theory and Algebra, Academic Press, New York, 1977, (1977), 209-214. [Math. Rev. 58#539], [RNT I25-230]

1980s

1980

204. On a special function,
J. Number Theory 12 (1980), 20-26. [Math. Rev.81c:30006]

205. p-Adic Numbers and Their Functions [Book] (2nd edition of "Introduction to p-adic Numbers and Their Functions"),
Cambridge Tracts in Mathematics 76, Cambridge University Press, London/New York, (1981). [Math. Rev. 83i:12002], [RNT S02-201E]

206. On two definitions of the integral of a p-adic function,
Acta Arith. 47 (1980), 105-109. [Math. Rev. 82b:26024], [RNT Q25-281]

1981

207. On some irrational decimal fractions,
J. Number Theory 13 (1981), 268-269. [Math. Rev. 82j:10061], [RNT I15-233]

208. On a special non-linear functional equation,
Philos. Trans. Roy. Soc. London Ser. A 378 (1981), 155-178. [Math. Rev. 82m:10042], [RNT F10-229E]

1982

209. Fifty years as a mathematician,
J. Number Theory 14 (1982), 121-155. [Math. Rev. 84a:01051]
[Remark: The present publication list is a correction and extension of the one appearing here.]

210. On a special transcendental number,
Arithmétix 5 (1982), 18-32.
[Remark: Information bulletin of number theorists in France]

211. On the zeros of a special sequence of polynomials,
Math. Comp. 39 (1982), 207-212. [Math. Rev. 83k:12019]

1983

212. On a theorem in the geometry of numbers in a space of Laurent series,
J. Number Theory 17 (1983), 403-416. [Math. Rev. 85e:11043]

213. On the analytic solution of certain functional and difference equations,
Proc. Roy. Soc. London Ser. A 389 (1983), 1-13. [Math. Rev. 85e:30041]

214. Warum ich eine besondere Vorliebe für die Mathematik habe,
Jahresbericht d. Deutschen Math.-Verein. 85 (1983), 50-53. [Math. Rev. 84f:01073]
[Remark: Essay originally written in 1923.]

1984

215. On Thue's theorem,
Math. Scand. 55 (1984), 188-200. [Math. Rev. 86h:11030]

216. Some suggestions for further research,
Bull. Austral. Math. Soc. 29 (1984), 101-108. [Math. Rev. 85e:11043]

1986

217. (with D. H. Lehmer and A. J. van der Poorten) Integers with digits 0 or 1,
Math. Comp. 46 (1986), 683-689. [Math. Rev. 87e:11017]

218. A new transfer principle in the geometry of numbers,
J. Number Theory 24 (1986), 20-34. [Math. Rev. 88e:11054]

219. The successive minima in the geometry of numbers and the distinction between algebraic and transcendental numbers,
J. Number Theory 22 (1986), 147-160. [Math. Rev. 87d:11043]

1987

220. On two analytic functions,
Acta. Arith. XLIX (1987), 15-20. [Math. Rev. 89f:30006]

1989

221. The representation of squares to the base 3,
Acta Arith. LIII (1989), 99-106.

1990s

1991

222. Fifty years as a mathematician II,
J. Austral. Math. Soc. (Series A) 51 (1991), 366-380.

Math 163 Mathematica Project 2 Answer

Source: https://carma.newcastle.edu.au/resources/mahler/collected.html

Posted by: wilkinsmusection.blogspot.com

Share this post