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Analytic Number Theory

Analytic Number Theory
Essays in Honour of Klaus Roth

Roger Baker, Glyn Harman, William D. Banks, Igor E. Shparlinski, József Beck, Wesley Pegden, Sujith Vijay, Victor Beresnevich, Vasily Bernik, Maurice Dodson, Sanju Velani, J. Bourgain, T. D. Browning, D. R. Heath-Brown, Jörg Brüdern, Yann Bugeaud, Bernard Chazelle, William Chen, Giancarlo Travaglini, Harold G. Diamond, H. Halberstam, P. D. T. A. Elliott, Ben Green, Terence Tao, Nils Hebbinghaus, Tomasz Schoen, Anand Srivastav, H. A. Helfgott, A. Venkatesh, C. Hooley, Nicholas M. Katz, Sergei Konyagin, A. Lasjaunias, Michel Laurent, Helmut Maier, David Masser, Bernard de Mathan, Melvyn B. Nathanson, Erich Novak, Henryk Wózniakowski, A. Sárközy, C. L. Stewart, A. Schinzel, Jerzy Kaczorowski, Wolfgang M. Schmidt, Dinesh S. Thakur, R. C. Vaughan, Michel Waldschmidt, Umberto Zannier
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  • Date Published: February 2009
  • availability: In stock
  • format: Hardback
  • isbn: 9780521515382

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About the Authors
  • 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.

    • Contains 32 contributions from leading figures in the field of number theory and many related areas
    • Explores the impact of Klaus Roth's research across a number of mathematical fields, including sieve theory and diophantine approximations
    • An extensive list of references makes this a valuable source for all research mathematicians
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    Product details

    • Date Published: February 2009
    • format: Hardback
    • isbn: 9780521515382
    • length: 510 pages
    • dimensions: 236 x 156 x 31 mm
    • weight: 0.83kg
    • contains: 1 b/w illus. 5 tables
    • availability: In stock
  • Table of Contents

    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 α1x1 . . . α1xn = 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 Ρ1 Umberto Zannier.

  • Editors

    W. W. L. Chen, Macquarie University, Sydney
    W. W. L. Chen is Emeritus Professor of Mathematics in the Department of Mathematics at Macquarie University, Sydney.

    W. T. Gowers, University of Cambridge
    W. T. Gowers is Rouse Ball Professor of Mathematics in the Department of Pure Mathematics and Mathematical Statistics (DPMMS) at the University of Cambridge.

    H. Halberstam, University of Illinois, Urbana-Champaign
    H. Halberstam is Professor Emeritus in the Department of Mathematics at the University of Illinois, Urbana-Champaign.

    W. M. Schmidt, University of Colorado Boulder
    W. M. Schmidt is a Distinguished Professor Emeritus in the Department of Mathematics at the University of Colorado, Boulder.

    R. C. Vaughan, Pennsylvania State University
    R. C. Vaughan is Professor of Mathematics in the Department of Mathematics at Pennsylvania State University.

    Contributors

    Roger Baker, Glyn Harman, William D. Banks, Igor E. Shparlinski, József Beck, Wesley Pegden, Sujith Vijay, Victor Beresnevich, Vasily Bernik, Maurice Dodson, Sanju Velani, J. Bourgain, T. D. Browning, D. R. Heath-Brown, Jörg Brüdern, Yann Bugeaud, Bernard Chazelle, William Chen, Giancarlo Travaglini, Harold G. Diamond, H. Halberstam, P. D. T. A. Elliott, Ben Green, Terence Tao, Nils Hebbinghaus, Tomasz Schoen, Anand Srivastav, H. A. Helfgott, A. Venkatesh, C. Hooley, Nicholas M. Katz, Sergei Konyagin, A. Lasjaunias, Michel Laurent, Helmut Maier, David Masser, Bernard de Mathan, Melvyn B. Nathanson, Erich Novak, Henryk Wózniakowski, A. Sárközy, C. L. Stewart, A. Schinzel, Jerzy Kaczorowski, Wolfgang M. Schmidt, Dinesh S. Thakur, R. C. Vaughan, Michel Waldschmidt, Umberto Zannier

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