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.
Klaus Roth at 80
1 Numbers with a large prime factor II by Roger Baker and Glyn Harman 1
2 Character sums with Beatty sequences on Burgess-type intervals by William D. Banks and Igor E. Shparlinski 15
3 The Hales-Jewett number is exponential: game-theoretic consequences by Jozsef Beck and Wesley Pegden and Sujith Vijay 22
4 Classical metric diophantine approximation revisited by Victor Beresnevich and Vasily Bernik and Maurice Dodson and Sanju Velani 38
5 The sum-product phenomenon and some of its applications by J. Bourgain 62
6 Integral points on cubic hypersurfaces by T. D. Browning and D. R. Heath-Brown 75
7 Binary additive problems and the circle method, multiplicative sequences and convergent sieves by Jorg Brudern 91
8 On the convergents to algebraic numbers by Yann Bugeaud 133
9 Complexity bounds via Roth's method of orthogonal functions by Bernard Chazelle 144
10 Some of Roth's ideas in discrepancy theory by William Chen and Giancarlo Travaglini 150
11 Congruences and ideals by Harold G. Diamond and H. Halberstam 164
12 Elementary geometry of Hilbert spaces applied to abelian groups by P. D. T. A. Elliott 170
13 New bounds for Szemeredi's theorem II: a new bound for r[subscript 4](N) by Ben Green and Terence Tao 180
14 One-sided discrepancy of linear hyperplanes in finite vector spaces by Nils Hebbinghaus and Tomasz Schoen and Anand Srivastav 205
15 How small must ill-distributed sets be? by H. A. Helfgott and A. Venkatesh 224
16 On the power-free values of polynomials in two variables by C. Hooley 235
17 On a question of Browning and Heath-Brown by Nicholas M. Katz 267
18 Good distribution of values of sparse polynomials modulo a prime by Sergei Konyagin 289
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