Analytic Number Theory
Essays in Honour of Klaus Roth

A collection of papers inspired by the work of Britain's first Fields Medallist, Klaus Roth.

W. W. L. Chen (Edited by), W. T. Gowers (Edited by), H. Halberstam (Edited by), W. M. Schmidt (Edited by), R. C. Vaughan (Edited by)

9780521515382, Cambridge University Press

Hardback, published 19 February 2009

510 pages, 1 b/w illus. 5 tables
23.6 x 15.6 x 3.1 cm, 0.83 kg

Klaus Roth's pioneering research in the field of number theory has led to important and substantial breakthroughs in many areas, including sieve theory, diophantine approximation, and irregularities of distribution. His work on the Thue-Siegel-Roth Theorem earned him a Fields Medal in 1958 - the first British mathematician to receive the honour. Analytic Number Theory: Essays in Honour of Klaus Roth comprises 32 essays from close colleagues and leading experts in those fields in which he has worked, and provides a great insight into the historical development of the subject matter and the importance of Roth's contributions to number theory and beyond. His influence is also discussed in relation to more recent mathematical advances. Extensive lists of references make this a valuable source for research mathematicians in many areas, an introductory overview of the subject for beginning research students, and a fitting long-awaited tribute to a great mathematician.

Preface
Acknowledgments
Klaus Roth at 80
Numbers with a large prime factor II Roger Baker and Glyn Harman
Character sums with Beatty sequences on Burgess-type intervals William D. Banks and Igor E. Shparlinski
The Hales-Jewett number is exponential: game-theoretic consequences József Beck, Wesley Pegden and Sujith Vijay
Classical metric diophantine approximation revisited Victor Beresnevich, Vasily Bernik, Maurice Dodson and Sanju Velani
The sum-product phenomenon and some of its applications J. Bourgain
Integral points on cubic hypersurfaces T. D. Browning and D. R. Heath-Brown
Binary additive problems and the circle method, multiplicative sequences and convergent sieves Jörg Brüdern
On the convergents to algebraic numbers Yann Bugeaud
Complexity bounds via Roth's method of orthogonal functions Bernard Chazelle
Some of Roth's ideas in discrepancy theory William Chen and Giancarlo Travaglini
Congruences and ideals Harold G. Diamond and H. Halberstam
Elementary geometry of Hilbert spaces applied to abelian groups P. D. T. A. Elliott
New bounds for Szemerédi's theorem II: a new bound for r4(N) Ben Green and Terence Tao
One-sided discrepancy of linear hyperplanes in finite vector spaces Nils Hebbinghaus, Tomasz Schoen and Anand Srivastav
How small must ill-distributed sets be? H. A. Helfgott and A. Venkatesh
On the power-free values of polynomials in two variables C. Hooley
On a question of Browning and Heath-Brown Nicholas M. Katz
Good distribution of values of sparse polynomials modulo a prime Sergei Konyagin
Diophantine approximation and continued fractions in power series fields A. Lasjaunias
On transfer inequalities in diophantine approximation Michel Laurent
On exponential sums with multiplicative coefficients Helmut Maier
Multiplicative dependence of values of algebraic functions David Masser
Linear forms in logarithms, and simultaneous diophantine approximation Bernard de Mathan
The Caccetta-Häggkvist conjecture and additive number theory Melvyn B. Nathanson
L2 discrepancy and multivariate integration Erich Novak and Henryk Wózniakowski
Irregularities of sequences relative to long arithmetic progressions A. Sárközy and C. L. Stewart
The number of solutions of a linear homogeneous congruence II A. Schinzel, with an appendix by Jerzy Kaczorowski
The diophantine equation ?1x1 . . . ?1xn = f (x1,…,xn) Wolfgang M. Schmidt
Approximation exponents for function fields Dinesh S. Thakur
On generating functions in additive number theory I R. C. Vaughan
Words and transcendence Michel Waldschmidt
Roth's theorem, integral points and certain ramified covers of ?1 Umberto Zannier.

Subject Areas: Number theory [PBH]