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Fifty years as a Mathematician. (English) Zbl 0482.10002


MSC:

11-03 History of number theory
01A70 Biographies, obituaries, personalia, bibliographies
11Hxx Geometry of numbers
11Jxx Diophantine approximation, transcendental number theory
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References:

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[26] Hlawka, E., Zur Geometrie der Zahlen, Math. Z., 49, 285-312 (1944) · Zbl 0028.20606
[27] Hermite, Ch, Sur la fonction exponentielle, Oeuvres, III, 150-181 (1873)
[28] Hermite, Ch, Sur les généralisations des fractions continues algébriques, Oeuvres, IV, 357-377 (1893)
[29] Liouville, J., Sur des classes très étendues de quantités dont la valeur n’est ni algébrique, ni même reductible à des irrationelles algébriques, C. R. Paris, 18, 910-911 (1844)
[30] Mignotte, M., Approximations rationelles de π et quelques autres nombres, Soc. Math. France, Suppl., Mém. No. 37, 121-132 (1974) · Zbl 0286.10017
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[32] Mordell, L. J., The product of three homogeneous linear forms, J. London Math. Soc., 17, 107-115 (1942) · Zbl 0028.11205
[33] Mordell, L. J., The minimum of a binary cubic form, I, J. 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, (Proc. London Math. Soc. (2), 48 (1945)), 339-390 · Zbl 0060.11805
[36] Remak, R., Vereinfachung eines Blichfeldtschen Beweises aus der Geometrie der Zahlen, Math. Z., 26, 694-699 (1927)
[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, (Symposia Math., IV. Symposia Math., IV, INDAM, Rome (1968), Academic Press: Academic Press London), 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)
[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., Approximation algebraischer Zahlen, Ges. Abh., I, No. 2, 6-46 (1921)
[46] Siegel, C. L., Über einige Anwendungen diophantischer Approximationen, Ges. Abh., I, No. 16, 209-266 (1929) · Zbl 0159.38101
[47] Siegel, C. L., Über Gitterpunkte in konvexen Körpern und ein damit zusammenhängendes Extremalproblem, Ges. Abh., I, No. 19, 311-325 (1935) · Zbl 0012.39502
[48] Siegel, C. L., A mean value theorem in the geometry of numbers, 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)
[50] Thue, A., Über Annäherungswerte algebraischer Zahlen, J. Reine Angew. Math., 135, 284-305 (1909)
[51] Weyl, H., On the geometry of numbers, (Proc. London Math. Soc. (2), 47 (1942)), 268-289 · Zbl 0028.34902
[52] On the translation properties of a simple class of arithmetical functions. On the translation properties of a simple class of arithmetical functions, J. Math. Phys., 6, 158-163 (1927)
[53] Über die Nullstellen der unvollständigen Gammafunktionen. Über die Nullstellen der unvollständigen Gammafunktionen, Dr. Dissertation Frankfurt. Über die Nullstellen der unvollständigen Gammafunktionen. Über die Nullstellen der unvollständigen Gammafunktionen, Dr. Dissertation Frankfurt, Palermo Rend., 54 (1930), printed in
[54] Über einen Satz von Mellin. Über einen Satz von Mellin, Math. Ann., 100, 384-398 (1928)
[55] Arithmetische Eigenschaftern der Lösungen einer Klasse von Funktionalgleichungen. 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. Uber die Nullstellen der abschnitte der hypergeometrischen Reihe, Math. Ann., 101, 267-274 (1929)
[57] Zur Fortsetzbarkeit gewisser Dirichletscher Reihen. Zur Fortsetzbarkeit gewisser Dirichletscher Reihen, Math. Ann., 102, 30-48 (1929)
[58] Über das Verschwinden von Potenzreihen mehrerer Veränderlichen in gewissen Punktfolgen. 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
[59] Arithmetische Eigenschaften einer Klasse transzendental-transzendenter Funktionen. Arithmetische Eigenschaften einer Klasse transzendental-transzendenter Funktionen, Math. Z., 32, 545-585 (1930), Papers which are related to the matter discussed in these notes
[60] Über Beziehungen zwischen der Zahl \(e\) und Liouvilleschen Zahlen. 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
[61] Ein Beweis der Thue-Siegelschen Satzes über die Approximation algebraischer Zahlen für binomische Gleichungen. 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
[62] Zur Approximation der Exponentialfunktion und des Logarithmus, I. 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. 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
[64] Zur Approximation der Exponentialfunktion und des Logarithmus, II. 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 · Zbl 0003.38805
[65] Ein Beweis der Transzendenz der \(P\)-adischen Exponentialfunktion. 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. Einige Satze über Diophantische Approximationen, Jber. Deutsche Math. Ver. (1932), 74-76 cursiv. Papers which are related to the matter discussed in these notes
[67] Über die Darstellung von Zahlen durch Binärformen höheren Grades, (Kongressbericht. Kongressbericht, Zürich, 1932 (1932)), Papers which are related to the matter discussed in these notes
[68] Zur Approximation algebraischer Zahlen, I. Zur Approximation algebraischer Zahlen, I, Math. Ann., 107, 691-730 (1933), Papers which are related to the matter discussed in these notes · Zbl 0006.10502
[69] Zur Approximation algebraischer Zahlen, II. Zur Approximation algebraischer Zahlen, II, Math. Ann., 108, 37-55 (1933), Papers which are related to the matter discussed in these notes · Zbl 0006.15604
[70] Zur Approximation algebraischer Zahlen, III. Zur Approximation algebraischer Zahlen, III, Acta Math., 62, 91-166 (1933), Papers which are related to the matter discussed in these notes · Zbl 0008.19801
[71] Über den grössten Primteiler der Polynome \(x^2\) ± 1. Über den grössten Primteiler der Polynome \(x^2\) ± 1, Archiv Math. og. Naturv., 41 (1933)
[72] Über die rationalen Punkte auf Kurven vom Geschlecht I. 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. 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. Über die Darstellungen einer Zahl als Summe von drei Biquadraten, Mathematica (Zutphen), 3 (1934) · Zbl 0009.29803
[75] Über die Approximation \(P\)-adischer Zahlen. Über die Approximation \(P\)-adischer Zahlen, Jber. Deutsche Math. Ver., 250-255 (1934), Papers which are related to the matter discussed in these notes · Zbl 0010.19801
[76] Eine arithmetische Eigenschaft der recurrierenden Reihen. 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. 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. Über eine Klasseneinteilung der transzendenten Zahlen, Mathematica (Zutphen), 3B (1935), Papers which are related to the matter discussed in these notes
[79] (On lattice points on curves of genus I. On lattice points on curves of genus I, Proc. London Math. Soc., 39 (1935)), 431-466, Papers which are related to the matter discussed in these notes · Zbl 0012.15006
[80] On the division values of Weierstrass’s \(p\)-function. 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. 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. Über die Taylorkoeffizienten rationaler Funktionen, Akad. Amsterdam, 38, 51-60 (1935)
[83] Über den grössten Primteiler spezieller Polynome 2. Grades. Über den grössten Primteiler spezieller Polynome 2. Grades, Arch. Math. og Naturv., 41, 3-26 (1935)
[84] Ein neues Prinzip für Transzendenzbeweise. Ein neues Prinzip für Transzendenzbeweise, Akad. Amsterdam, 38, 864-871 (1935), Papers which are related to the matter discussed in these notes
[85] Über Pseudobewertungen, I. Über Pseudobewertungen, I, Acta Math., 66, 79-119 (1935)
[86] Eine arithmetische Eigenschaft der kubischen Formen. Eine arithmetische Eigenschaft der kubischen Formen, Nieuw Arch. Wisk. (1936) · Zbl 0014.00802
[87] Über Polygone mit In- oder Umkreis. Über Polygone mit In- oder Umkreis, Mathematica (Zutphen), 4A (1936)
[88] Über Pseudobewertungen, II. Über Pseudobewertungen, II, Acta Math., 67, 51-80 (1936) · Zbl 0014.34003
[89] Über Pseudobewertungen, III. Über Pseudobewertungen, III, Acta Math., 67, 283-328 (1936) · Zbl 0016.00504
[90] Über Pseudobewertungen, Ia. Über Pseudobewertungen, Ia, Akad. Amsterdam, 39, 57-65 (1936) · Zbl 0013.14703
[91] Note on Hypothesis \(K\) of Hardy and Littlewood. Note on Hypothesis \(K\) of Hardy and Littlewood, J. London Math. Soc., 11, 136-138 (1936)
[92] Ein Analog zu einem Schneiderschen Satz, I. 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. Ein Analog zu einem Schneiderschen Satz, II, Akad. Amsterdam, 39, 729-737 (1936), Papers which are related to the matter discussed in these notes · Zbl 0014.20503
[94] Über die Annäherung algebraischer Zahlen durch periodische Algorithmen. 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 · Zbl 0017.05701
[95] Neuer Beweis eines Satzes von A. Khintchine. Neuer Beweis eines Satzes von A. Khintchine, Mat. Sb., 43, 1, 962-963 (1937)
[96] Über die Dezimalbruchentwicklung gewisser Irrationalzahlen. Über die Dezimalbruchentwicklung gewisser Irrationalzahlen, Mathematica (Zutphen), 4B (1937), Papers which are related to the matter discussed in these notes · Zbl 0018.11102
[97] Arithmetische Eigenschaften ener Klasse von Dezimalbrüchen. Arithmetische Eigenschaften ener Klasse von Dezimalbrüchen, Akad. Amsterdam, 40, 421-428 (1937), Papers which are related to the matter discussed in these notes · Zbl 0017.05602
[98] On the number of integers which can be represented by a binary form. 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
[99] On a special class of Diophantine equations, I. On a special class of Diophantine equations, I, J. London Math. Soc., 13, 169-173 (1938) · Zbl 0019.25005
[100] On a special class of Diophantine equations, II. On a special class of Diophantine equations, II, J. London Math. Soc., 13, 173-177 (1938) · Zbl 0019.25006
[101] Ein \(p\)-adisches Analog zu einem Satz von Tchebycheff. 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. 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 · Zbl 0019.25004
[103] Über einen Satz von Th. Schneider. Über einen Satz von Th. Schneider, Acta Arith., 3, 94-101 (1938), Papers which are related to the matter discussed in these notes
[104] A theorem on inhomogeneous Diophantine inequalities. A theorem on inhomogeneous Diophantine inequalities, Akad. Amsterdam, 41, 634-637 (1938), Papers which are related to the matter discussed in these notes
[105] Eine Bemerkung zum Beweis der Eulerschen Summenformel. 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. 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
[107] Ein Übertragungsprinzip für Linearformen. 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. 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. 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. Über polare konvexe Körper, Mathematica (Zutphen), 7B (1939)
[111] On the solutions of algebraic differential equations. On the solutions of algebraic differential equations, Akad. Amsterdam, 42, 61-63 (1939) · Zbl 0021.02703
[112] A proof of Hurwitz’s theorem. A proof of Hurwitz’s theorem, Mathematica (Zutphen), 8B (1939)
[113] Bemerkungen über die Diophantischen Eigenschaften der reellen Zahlen. Bemerkungen über die Diophantischen Eigenschaften der reellen Zahlen, Mathematica (Zutphen), 8B, 11-16 (1939)
[114] On the minimum of positive definite Hermitian forms. On the minimum of positive definite Hermitian forms, J. London Math. Soc., 14, 137-143 (1939)
[115] On a geometric representation of \(p\)-adic integers. 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. 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). Note on the sequence √\(n\) (mod 1), Nieuw Arch. Wisk., 20, 176-178 (1940)
[118] On the exceptional points on cubic curves. On the exceptional points on cubic curves, J. London Math. Soc., 15, 32-43 (1940), (with G. Billing) · Zbl 0026.19901
[119] On a special functional equation. On a special functional equation, J. London Math. Soc., 15, 115-123 (1940)
[120] Über Polynome mit ganzen rationalen Koeffizienten. Über Polynome mit ganzen rationalen Koeffizienten, Mathematica (Zutphen), 8B, 173-182 (1940) · Zbl 0022.30104
[121] On reduced positive definite ternary quadratic forms. 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. On a property of positive definite ternary quadratic forms, J. London Math. Soc., 15, 305-320 (1940)
[123] A analogue to Minkowski’s Geometry of Numbers in a field of series. 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
[124] (On ideals in the Caylay-Dickson algebra. On ideals in the Caylay-Dickson algebra, Proc. Irish Acad., 48 (1942)), 123-133 · Zbl 0061.05301
[125] Remarks on ternary Diophantine equations. Remarks on ternary Diophantine equations, Amer. Math. Monthly, 49, 472-479 (1942) · Zbl 0060.11902
[126] Note on lattice points in star domains. 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. 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 · Zbl 0060.11802
[128] (A problem on Diophantine approximation in quaternions. A problem on Diophantine approximation in quaternions, Proc. London Math. Soc., 48 (1944)), 435-466 · Zbl 0060.11901
[129] On the densest packing of circles. On the densest packing of circles, Amer. Math. Monthly, 51, 261-270 (1944), (with B. Segre) · Zbl 0060.11707
[130] On a theorem of Minkowski on lattice points in non-convex bodies. 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] (On lattice points in the domain |xy| ≤ 1, |\(x + y\)| ≤ √5, and applications to asymptotic formulae in lattice point theory, I. On lattice points in the domain |xy| ≤ 1, |\(x + y\)| ≤ √5, and applications to asymptotic formulae in lattice point theory, I, Proc. Cambridge Phil. Soc., 40 (1944)), 107-116, Papers which are related to the matter discussed in these notes · Zbl 0060.11709
[132] (On lattice points in the domain |xy| ≤ 1, |\(x + y\)| ≤ √5, and applications to asymptotic formulae in lattice point theory, II. On lattice points in the domain |xy| ≤ 1, |\(x + y\)| ≤ √5, and applications to asymptotic formulae in lattice point theory, II, Proc. Cambridge Phil. Soc., 40 (1944)), 116-120, Papers which are related to the matter discussed in these notes · Zbl 0060.11709
[133] On a theorem of B. Segre. On a theorem of B. Segre, Duke Math. J., 12, 367-371 (1945), Papers which are related to the matter discussed in these notes · Zbl 0060.11808
[134] (Lattice points in two-dimensional star domains, I. Lattice points in two-dimensional star domains, I, Proc. London Math. Soc., 49 (1946)), 128-157, Papers which are related to the matter discussed in these notes · Zbl 0060.11712
[135] (Lattice points in two-dimensional star domains, II. Lattice points in two-dimensional star domains, II, Proc. London Math. Soc., 49 (1946)), 158-167, Papers which are related to the matter discussed in these notes · Zbl 0060.11712
[136] (Lattice points in two-dimensional star domains, III. Lattice points in two-dimensional star domains, III, Proc. London Math. Soc., 49 (1946)), 168-183, Papers which are related to the matter discussed in these notes · Zbl 0060.11712
[137] On lattice points in a cylinder. On lattice points in a cylinder, Quart. J., 17, 15-18 (1946), Papers which are related to the matter discussed in these notes · Zbl 0060.11708
[138] (On lattice points in \(n\)-dimensional star bodies, I (Existence theorems). On lattice points in \(n\)-dimensional star bodies, I (Existence theorems), Proc. Roy. Soc. A, 187 (1946)), 151-187, Papers which are related to the matter discussed in these notes · Zbl 0060.11710
[139] (On lattice points in \(n\)-dimensional star bodies, II (Reducibility theorems). On lattice points in \(n\)-dimensional star bodies, II (Reducibility theorems), Proc. Akad. Amsterdam, 49 (1946)), 622-633, Papers which are related to the matter discussed in these notes
[140] Simultaneous Diophantine approximation. Simultaneous Diophantine approximation, Duke Math. J., 13, 105-111 (1946), Papers which are related to the matter discussed in these notes · Zbl 0060.12000
[141] Lattice points in star bodies. Lattice points in star bodies, Rev. Univ. Nac. Tacuman, 5, 113-124 (1946), Papers which are related to the matter discussed in these notes · Zbl 0060.11801
[142] On the theorem of Minkowski-Hlawka. 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. On reduced positive definite quarternary quadratic forms, Nieuw Arch. Wisk., 22, 207-212 (1946) · Zbl 0060.11812
[144] A remark on the continued fractions of conjugate algebraic numbers. A remark on the continued fractions of conjugate algebraic numbers, Simon Stevin, 25, 45-48 (1947) · Zbl 0030.02103
[145] (On irreducible convex domains. On irreducible convex domains, Proc. Akad. Amsterdam, 50 (1947)), 98-107, Papers which are related to the matter discussed in these notes · Zbl 0036.31001
[146] (On the area and the densest packing of convex domains. On the area and the densest packing of convex domains, Proc. Akad. Amsterdam, 50 (1947)), 108-118, Papers which are related to the matter discussed in these notes · Zbl 0036.31002
[147] On the generating function of integers with a missing digit. 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. On the adjoint of a positive definite ternary quadratic form, Sci. Rec. Academia Sinica, 2, 21-31 (1947)
[149] (On the minimum determinant and the circumscribed hexagons of a convex domain. On the minimum determinant and the circumscribed hexagons of a convex domain, Proc. Akad. Amsterdam, 50 (1947)), 692-703, Papers which are related to the matter discussed in these notes · Zbl 0045.32804
[150] On the minimum of a pair of positive definite Hermitean forms. 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 · Zbl 0031.15503
[151] On the admissible lattices of automorphic star bodies. 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] (On lattice points in polar reciprocal convex domains. On lattice points in polar reciprocal convex domains, Proc. Akad. Amsterdam, 51 (1948)), 482-485, Papers which are related to the matter discussed in these notes · Zbl 0039.04001
[153] Sui determinate minimi delle sezione di un corpo convesso. 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 · Zbl 0032.27005
[154] On the successive minima of a bounded star domain. 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 · Zbl 0033.16802
[155] On the critical lattices of arbitrary point sets. 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 · Zbl 0037.17302
[156] (On the minimum determinant of a special point set. On the minimum determinant of a special point set, Proc. Akad. Amsterdam, 52 (1949)), 633-642, Papers which are related to the matter discussed in these notes · Zbl 0033.10606
[157] On the theorem of Liouville in fields of positive characteristic. 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] (On Dyson’s improvement of the Thue-Siegel theorem. On Dyson’s improvement of the Thue-Siegel theorem, Proc. Akad. Amsterdam, 52 (1949)), 1175-1184, Papers which are related to the matter discussed in these notes · Zbl 0039.04302
[159] On lattice points in a convex decagon. 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. 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 · Zbl 0039.04301
[161] On the arithmetic on algebraic curves, (Seminar on Algebra and Number Theory. Seminar on Algebra and Number Theory, Chicago, 1949 (1949)), 28-32
[162] On algebraic relations between two units of an algebraic field, (Paris Congress on Algebra and Number Theory. Paris Congress on Algebra and Number Theory, 1949 (1949)), 47-56
[163] On a theorem of Dyson. On a theorem of Dyson, Mat. Sb., 26, 457-462 (1950), [Russian] Papers which are related to the matter discussed in these notes · Zbl 0038.19001
[164] Geometry of numbers, (lectures given at the University of Colorado in the summer of 1950 (1950)), Papers which are related to the matter discussed in these notes
[165] Farey sections in \(k(i)\) and \(k(p)\). Farey sections in \(k(i)\) and \(k(p)\), Trans. Roy. Soc. A, 243, 585-626 (1951), (with J. W. S. Cassels and W. Ledermann) · Zbl 0043.05205
[166] On the generating function of the integers with a missing digit. On the generating function of the integers with a missing digit, J. Indian Math. Soc., 15A, 34-40 (1951), (translation of (96)) · Zbl 0043.05301
[167] On a question in elementary geometry. On a question in elementary geometry, Simon Stevin, 28, 90-97 (1951) · Zbl 0043.35603
[168] On the lattice determinant of two particular point sets. 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 · Zbl 0050.27501
[169] On the approximation of logarithms of algebraic numbers. 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] (On the approximation of π. On the approximation of π, Proc. Akad. Amsterdam A, 56 (1953)), 30-42, Papers which are related to the matter discussed in these notes · Zbl 0053.36105
[171] Over een Maximumprobleem uit de Rekenkunde. Over een Maximumprobleem uit de Rekenkunde, Nieuw Arch. Wisk., 1, 3, 1-15 (1953), (with J. Popken) · Zbl 0051.00709
[172] On the greatest prime factor of \(ax^m + by^n \). On the greatest prime factor of \(ax^m + by^n \), Nieuw Arch. Wisk., 1, 3, 113-122 (1953), Papers which are related to the matter discussed in these notes · Zbl 0050.26804
[173] On the composition of pseudo-valuations. On the composition of pseudo-valuations, Nieuw Arch. Wisk. (3), 1, 161-198 (1953), (with P. Cohn) · Zbl 0051.02802
[174] A problem in elementary geometry. A problem in elementary geometry, Math. Gaz., 37, 241-243 (1954) · Zbl 0056.38703
[175] On a problem in the geometry of numbers. 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. On a problem in Diophantine approximations, Arch. Math., 6, 208-214 (1955) · Zbl 0064.04402
[177] (On compound convex bodies, I. On compound convex bodies, I, Proc. London Math. Soc. (3), 5 (1955)), 358-379, Papers which are related to the matter discussed in these notes · Zbl 0065.28002
[178] (On compound convex bodies, II. On compound convex bodies, II, Proc. London Math. Soc. (3), 5 (1955)), 380-384, Papers which are related to the matter discussed in these notes · Zbl 0065.28002
[179] (The \(p\) th compound of a sphere. The \(p\) th compound of a sphere, Proc. London Math. Soc. (3), 5 (1955)), 385-391, Papers which are related to the matter discussed in these notes · Zbl 0066.14505
[180] On the minima of compound quadratic forms. 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. 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] (On the Taylor coefficients of rational functions. On the Taylor coefficients of rational functions, Proc. Cambridge Phil. Soc., 52 (1956)), 39-48, Papers which are related to the matter discussed in these notes · Zbl 0070.04004
[183] (Invariant matrices and the geometry of numbers. Invariant matrices and the geometry of numbers, Proc. Roy. Soc. Edinburgh A, 64 (1956)), 223-238, Papers which are related to the matter discussed in these notes · Zbl 0074.27404
[184] A property of the star domain |xy| ≤ 1. 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. 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 · Zbl 0071.27402
[186] On the fractional parts of the powers of a rational number, II. 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 · Zbl 0208.31002
[187] (A matrix representation of the primitive residue classes (mod 2n). A matrix representation of the primitive residue classes (mod 2n), Proc. Amer. Math. Soc., 8 (1957)), 525-531 · Zbl 0079.01301
[188] A factorial series for the rational multiples of \(e\). A factorial series for the rational multiples of \(e\), Math. Gaz., 42, 13-16 (1958) · Zbl 0080.03601
[189] On the Chinese remainder theorem. 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. An interpolation series for continuous functions of a \(p\)-adic variable, J. Reine Angew. Math., 199, 23-34 (1958) · Zbl 0080.03504
[191] An arithmetic property of groups of linear transformations. An arithmetic property of groups of linear transformations, Acta Arith., 5, 197-203 (1959) · Zbl 0089.26803
[192] On a theorem of Shidlovski, (lectures given at the Math. Centrum, Amsterdam, December 1959 (1959)), Papers which are related to the matter discussed in these notes
[193] (On a theorem by E. Bombieri. On a theorem by E. Bombieri, Proc. Akad. Amsterdam, 63 (1960)), 243-253 · Zbl 0094.02902
[194] An application of Jensen’s formula to polynomials. An application of Jensen’s formula to polynomials, Mathematika, 7, 98-100 (1960) · Zbl 0099.25003
[195] (On the zeros of the derivative of a polynomial. On the zeros of the derivative of a polynomial, Proc. Royal Soc. A, 264 (1961)), 145-154 · Zbl 0109.25005
[196] A correction to the paper “An interpolation series for continuous functions of a \(p\)-adic variable”. 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] (Lectures on Diophantine Approximations, I, \(g\)-adic Numbers and Roth’s Theorem (1961), Univ. of Notre Dame Press: Univ. of Notre Dame Press Notre Dame, Ind), 188, Papers which are related to the matter discussed in these notes
[198] On the representation of integers by binary forms. 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 · Zbl 0102.03601
[199] On some inequalities for polynomials in several variables. On some inequalities for polynomials in several variables, J. London Math. Soc., 37, 341-344 (1962) · Zbl 0105.06301
[200] Geometric number theory, (lectures given at the University of Notre Dame in 1962 (1962)), 151, Papers which are related to the matter discussed in these notes
[201] On two extremum properties of polynomials. 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. 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 · Zbl 0144.28703
[203] Periodic algorithms for algebraic number fields (mimeographed lecture notes). 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. 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. An inequality for the discriminant of a polynomial, Michigan Math. J., 11, 257-262 (1964) · Zbl 0135.01702
[206] Transcendental numbers. Transcendental numbers, J. Austral. Math. Soc., 4, 393-396 (1964), Papers which are related to the matter discussed in these notes · Zbl 0131.04903
[207] An inequality for a pair of polynomials that are relatively prime. 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. 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. Equations in free metabelian groups, Michigan Math. J., 12, 417-419 (1965), (with G. Baumschlag) · Zbl 0135.04501
[210] Arithmetic properties of lacunary power series with integral coefficients. 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. A remark on recursive sequences, J. Math. Sci. Delhi, 1, 12-17 (1966) · Zbl 0158.29503
[212] Transcendental numbers, Encyclopaedia Brittannica article (1966)
[213] A remark on Kronecker’s theorem. A remark on Kronecker’s theorem, Enseign. Math., 12, 183-189 (1966) · Zbl 0154.04702
[214] On the approximation of real numbers by roots of integers. On the approximation of real numbers by roots of integers, Acta Arith., 12, 315-320 (1967), Papers which are related to the matter discussed in these notes · Zbl 0154.04703
[215] Applications of some formulae by Hermite to the approximation of exponentials and logarithms. Applications of some formulae by Hermite to the approximation of exponentials and logarithms, Math. Ann., 168, 200-227 (1967), Papers which are related to the matter discussed in these notes · Zbl 0144.29201
[216] On a class of entire functions. On a class of entire functions, Acta Math. Acad. Sci. Hungar., 18, 83-96 (1967) · Zbl 0207.35602
[217] On a theorem by A. B. Shidlovski. On a theorem by A. 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 \(32\). An unsolved problem on the powers of \(32\), J. Austral. Math. Soc., 8, 313-321 (1968) · Zbl 0155.09501
[219] Perfect systems. Perfect systems, Compositio Math., 19, 95-166 (1968), Papers which are related to the matter discussed in these notes · Zbl 0168.31303
[220] (Applications of a theorem by A. B. Shidlovski. Applications of a theorem by A. B. Shidlovski, Proc. Roy. Soc. A, 305 (1968)), 149-173, Papers which are related to the matter discussed in these notes · Zbl 0164.05702
[221] Remarks on a paper by W. Schwarz. 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 · Zbl 0184.07602
[222] On algebraic differential equations satisfied by automorphic functions. On algebraic differential equations satisfied by automorphic functions, J. Austral. Math. Soc., 10, 445-450 (1969) · Zbl 0207.08302
[223] Lectures on transcendental numbers, (Summer Institute on Number Theory at Stony Brook, 1969. Summer Institute on Number Theory at Stony Brook, 1969, Amer. Math. Soc. Symp., 20 (1969)), 248-274, Papers which are related to the matter discussed in these notes · Zbl 0213.32703
[224] A lecture on the geometry of numbers of convex bodies. 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 · Zbl 0212.06904
[225] A generalization of Farey sequences. A generalization of Farey sequences, J. Number Theory, 3, 364-370 (1971), (with H. Brown) · Zbl 0221.10014
[226] On formal power series as integrals of algebraic differential equations. On formal power series as integrals of algebraic differential equations, Rend. Accad. Naz. dei Lincei (8), 50, 36-49 (1971)
[227] A remark on algebraic differential equations. A remark on algebraic differential equations, Rend. Accad. Naz. dei Lincei (8), 50, 174-184 (1971)
[228] An arithmetical remark on entire functions. An arithmetical remark on entire functions, Bull. Austral. Math. Soc., 5, 191-195 (1971) · Zbl 0219.30013
[229] An elementary existence theorem for entire functions. An elementary existence theorem for entire functions, Bull. Austral. Math. Soc., 5, 415-419 (1971) · Zbl 0219.30014
[230] On the order function of a transcendental number. On the order function of a transcendental number, Acta Arith., 18, 63-76 (1971), Papers which are related to the matter discussed in these notes · Zbl 0217.03903
[231] Transcendental numbers, I. Transcendental numbers, I, Mat. Lapok, 22, 31-50 (1971), [Hungarian] Papers which are related to the matter discussed in these notes · Zbl 0255.10037
[232] Transcendental numbers, II. Transcendental numbers, II, Mat. Lapok, 23, 13-23 (1972), [Hungarian] Papers which are related to the matter discussed in these notes
[233] On the coefficients of the \(2^n\) th transformation polynomial for \(j(ω)\). On the coefficients of the \(2^n\) th transformation polynomial for \(j(ω)\), Acta Arithm., 21, 89-97 (1972) · Zbl 0257.10013
[234] The classification of transcendental numbers. The classification of transcendental numbers, Bull. Amer. Math. Soc., 175-179 (1973), Papers which are related to the matter discussed in these notes · Zbl 0266.10029
[235] (Introduction to \(p\)-adic Numbers and Their Functions, Vol. 64 (1973), Cambridge Univ. Press: Cambridge Univ. Press London/New York), Cambridge Tract in Mathematics · Zbl 0249.12015
[236] Arithmetical properties of the digits of the multiples of an irrational number. Arithmetical properties of the digits of the multiples of an irrational number, Bull. Austral. Math. Soc., 8, 191-203 (1973) · Zbl 0248.10024
[237] On a class of Diophantine inequalities. On a class of Diophantine inequalities, Bull. Austral. Math. Soc., 8, 247-259 (1973) · Zbl 0254.10016
[238] A \(p\)-adic analogue of a theorem by J. Popken. A \(p\)-adic analogue of a theorem by J. Popken, J. Austral. Math. Soc., 16, 176-184 (1973) · Zbl 0271.13014
[239] On the coefficients of the transformation polynomials of the modular function. On the coefficients of the transformation polynomials of the modular function, Bull. Austral. Math. Soc., 10, 197-218 (1974) · Zbl 0269.10013
[240] On rational approximations of the exponential function at rational points. On rational approximations of the exponential function at rational points, Bull. Austral. Math. Soc., 10, 325-335 (1974) · Zbl 0274.10036
[241] Polar analogues of two theorems by Minkowski. Polar analogues of two theorems by Minkowski, Bull. Austral. Math. Soc., 11, 121-129 (1974) · Zbl 0277.10022
[242] (On the digits of the multiples of an irrational \(p\)-adic number. On the digits of the multiples of an irrational \(p\)-adic number, Proc. Cambridge Phil. Soc., 76 (1974)), 417-422 · Zbl 0291.10011
[243] How I became a mathematician. How I became a mathematician, Amer. Math. Monthly, 81, 981-983 (1974) · Zbl 0288.01027
[244] On a paper by A. Baker on the approximation of rational powers of \(e\). On a paper by A. 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. 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. 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. 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. An addition to a note of mine, Bull. Austral. Math. Soc., 14, 397-398 (1976) · Zbl 0319.10036
[249] A theorem on Diophantine approximations. A theorem on Diophantine approximations, Bull. Austral. Math. Soc., 14, 463-465 (1976) · Zbl 0318.10022
[250] Bull. Austral. Math. Soc., 15, 477-478 (1976), Corrigendum · Zbl 0316.10022
[251] (Divis, B.; LeVeque, W. J., Lectures on Transcendental Numbers. Lectures on Transcendental Numbers, Lecture Notes in Mathematics No. 546 (1976), Springer-Verlag: Springer-Verlag Berlin/New York) · Zbl 0332.10019
[252] On a class of non-linear functional equations connected with modular functions. On a class of non-linear functional equations connected with modular functions, J. Austral. Math. Soc. Ser. A, 22, 65-118 (1976) · Zbl 0345.39002
[253] On a class of transcendental decimal fractions. On a class of transcendental decimal fractions, Comm. Pure Appl. Math., 29, 717-725 (1976) · Zbl 0339.10025
[254] On some special decimal fractions, (Number Theory and Algebra (1977), Academic Press: Academic Press New York), 209-214, 1977 · Zbl 0368.10009
[255] On a special function. On a special function, J. Number Theory, 12, 20-26 (1980) · Zbl 0429.30002
[256] \((p\)-Adic Numbers and Their Functions (1981), Cambridge Univ. Press: Cambridge Univ. Press London/New York), Cambridge Tracts in Mathematics No. 76 · Zbl 0444.12013
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