Analytic Number Theory: Essays in Honour of Klaus Roth Book

Klaus Roth at 80

1 Numbers with a large prime factor II Roger Baker Baker, Roger Glyn Harman Harman, Glyn 1

2 Character sums with Beatty sequences on Burgess-type intervals William D. Banks Banks, William D. Igor E. Shparlinski Shparlinski, Igor E. 15

3 The Hales-Jewett number is exponential: game-theoretic consequences Jozsef Beck Beck, Jozsef Wesley Pegden Pegden, Wesley Sujith Vijay Vijay, Sujith 22

4 Classical metric diophantine approximation revisited Victor Beresnevich Beresnevich, Victor Vasily Bernik Bernik, Vasily Maurice Dodson Dodson, Maurice Sanju Velani Velani, Sanju 38

5 The sum-product phenomenon and some of its applications J. Bourgain Bourgain, J. 62

6 Integral points on cubic hypersurfaces T. D. Browning Browning, T. D. D. R. Heath-Brown Heath-Brown, D. R. 75

7 Binary additive problems and the circle method, multiplicative sequences and convergent sieves Jorg Brudern Brudern, Jorg 91

8 On the convergents to algebraic numbers Yann Bugeaud Bugeaud, Yann 133

9 Complexity bounds via Roth's method of orthogonal functions Bernard Chazelle Chazelle, Bernard 144

10 Some of Roth's ideas in discrepancy theory William Chen Chen, William Giancarlo Travaglini Travaglini, Giancarlo 150

11 Congruences and ideals Harold G. Diamond Diamond, Harold G. H. Halberstam Halberstam, H. 164

12 Elementary geometry of Hilbert spaces applied to abelian groups P. D. T. A. Elliott Elliott, P. D. T. A. 170

13 New bounds for Szemeredi's theorem II: a new bound for r[subscript 4](N) Ben Green Green, Ben Terence Tao Tao, Terence 180

14 One-sided discrepancy of linear hyperplanes in finite vector spaces Nils Hebbinghaus Hebbinghaus, Nils Tomasz Schoen Schoen, TomaszAnand Srivastav Srivastav, Anand 205

15 How small must ill-distributed sets be? H. A. Helfgott Helfgott, H. A. A. Venkatesh Venkatesh, A. 224

16 On the power-free values of polynomials in two variables C. Hooley Hooley, C. 235

17 On a question of Browning and Heath-Brown Nicholas M. Katz Katz, Nicholas M. 267

18 Good distribution of values of sparse polynomials modulo a prime Sergei Konyagin Konyagin, Sergei 289

19 Diophantine approximation and continued fractions in power series fields A. Lasjaunias Lasjaunias, A. 297

20 On transfer inequalities in diophantine approximation Michel Laurent Laurent, Michel 306

21 On exponential sums with multiplicative coefficients Helmut Maier Maier, Helmut 315

22 Multiplicative dependence of values of algebraic functions David Masser Masser, David 324

23 Linear forms in logarithms, and simultaneous diophantine approximation Bernard de Mathan de Mathan, Bernard 334

24 The Caccetta Haggkvist conjecture and additive number theory Melvyn B. Nathanson Nathanson, Melvyn B. 347

25 L[subscript 2] discrepancy and multivariate integration Erich Novak Novak, Erich Henryk Wozniakowski Wozniakowski, Henryk 359

26 Irregularities of sequences relative to long arithmetic progressions A. Sarkozy Sarkozy, A. C. L. Stewart Stewart, C. L. 389

27 The number of solutions of a linear homogeneous congruence II A. Schinzel Schinzel, A. Jerzy Kaczorowski Kaczorowski, Jerzy 402

28 The diophantine equation [alpha][subscript 1][superscript x[subscript 1]] ... [alpha][subscript n][superscript x[subscript n]] = f(x[subscript 1], ..., x[subscript n]) Wolfgang M. Schmidt Schmidt, Wolfgang M. 414

29 Approximation exponents for function fields Dinesh S. Thakur Thakur, Dinesh S. 421

30 On generating functions in additive number theory I R. C. Vaughan Vaughan, R. C. 436

31 Words and transcendence Michel Waldschmidt Waldschmidt, Michel 449

32 Roth's theorem, integral points and certain ramified covers of P[subscript 1] Umberto Zannier Zannier, Umberto 471