The Legacy of Kurt Mahler

Michael Baake; Yann Bugeaud; Michael Coons

doi:10.4171/dms/8

BooksdmsCollected Volume

The Legacy of Kurt Mahler

A Mathematical Selecta

Editors

Michael Baake
Universität Bielefeld, Germany
Yann Bugeaud
Université de Strasbourg, France
Michael Coons
University of Newcastle, Australia

pp. 1–2
Preface
John H. Coates
pp. 3–11
Introduction to “Mahler Selecta”
Michael BaakeJonathan M. BorweinYann BugeaudMichael Coons
pp. 13–27
The mathematical works of Kurt Mahler
pp. 29–43
Mahler’s work on the geometry of numbers
Jan-Hendrik Evertse
pp. 45–56
Mahler’s measure for polynomials in several variables
David W. Boyd
pp. 57–77
Mahler’s work and algebraic dynamical systems
Douglas LindKlaus Schmidt
pp. 79–93
Mahler's classification of complex numbers
Masaaki AmouYann Bugeaud
pp. 95–122
Mahler's method
Boris Adamczewski
pp. 123–148
Mahler and transcendence: effective constructions in transcendental number theory
Yuri Nesterenko
pp. 149–171
Mahler’s work on Diophantine equations and subsequent developments
Jan-Hendrik EvertseKálmán GyőryCameron L. Stewart
pp. 173–178
The Skolem-Mahler-Lech theorem
Jason P. Bell
pp. 179–190
A Mahler miscellany
Yann BugeaudMichael Coons
pp. 191–216
Reprint: Arithmetic properties of solutions of a class of functional equations (1929)
Kurt Mahler
pp. 217–232
Reprint: On the vanishing of power series of several variables in special point sequences (1930)
Kurt Mahler
pp. 233–274
Reprint: Arithmetic properties of a class of transcendental-transcendent functions (1930)
Kurt Mahler
pp. 275–279
Reprint: On relations between the number $e$ and Liouville numbers (1930)
Kurt Mahler
pp. 281–314
Reprint: On the approximation of the exponential function and the logarithm. I, II (1931/32)
Kurt Mahler
pp. 315–324
Reprint: On the measure of all $S$ -numbers (1932)
Kurt Mahler
pp. 325–331
Reprint: A proof of transcendence of the $p$ -adic exponential function (1932)
Kurt Mahler
pp. 333–366
Reprint: On the approximation of algebraic numbers. I: On the greatest prime divisor of binary forms (1933)
Kurt Mahler
pp. 367–386
Reprint: On the approximation to algebraic numbers. II: On the number of representations of integers by binary forms (1933)
Kurt Mahler
pp. 387–398
Reprint: On the rational points on curves of genus one (1934)
Kurt Mahler
pp. 399–436
Reprint: On the lattice points on curves of genus $1$ (1935)
Kurt Mahler
pp. 437–448
Reprint: An arithmetic property of Taylor coefficients of rational functions (1935)
Kurt Mahler
pp. 449–457
Reprint: Ein neues Prinzip für Transzendenzbeweise (1935)
Jan PopkenKurt Mahler
pp. 459–474
Reprint: On the decimal expansion of certain irrational numbers (1937)
Kurt Mahler
pp. 475–481
Reprint: On the number of integers which can be represented by a binary form (1938)
Pál ErdősKurt Mahler
pp. 483–520
Reprint: On lattice points in $n$ -dimensional star bodies (1946)
Kurt Mahler
pp. 521–525
Reprint: On a theorem of Liouville in fields of positive characteristic (1949)
Kurt Mahler
pp. 527–555
Reprint: On the approximation of logarithms of algebraic numbers (1953)
Kurt Mahler
pp. 557–570
Reprint: On the approximation of $\pi$ (1953)
Kurt Mahler
pp. 571–593
Reprint: On compound convex bodies. I (1955)
Kurt Mahler
pp. 595–598
Reprint: On the fractional parts of the powers of a rational number. II (1957)
Kurt Mahler
pp. 599–614
Reprint: An interpolation series for continuous functions of a $p$ -adic variable (1958)
Kurt Mahler
pp. 615–618
Reprint: An application of Jensen's formula to polynomials (1960)
Kurt Mahler
pp. 619–623
Reprint: On some inequalities for polynomials in several variables (1962)
Kurt Mahler
pp. 625–629
Reprint: A remark on a paper of mine on polynomials (1964)
Kurt Mahler
pp. 631–637
Reprint: An inequality for the discriminant of a polynomial (1964)
Kurt Mahler
pp. 639–648
Reprint: An unsolved problem on the powers of $3/2$ (1968)
Kurt Mahler
pp. 649–659
Reprint: Remarks on a paper by W. Schwarz (1969)
Kurt Mahler
pp. 661–667
Reprint: On algebraic differential equations satisfied by automorphic functions (1969)
Kurt Mahler
pp. 669–677
Reprint: Some suggestions for further research (1984)
Kurt Mahler
p. 679
Acknowledgements
Michael BaakeYann BugeaudMichael Coons