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A Panorama of Number Theory or The View from Baker's Garden

A Panorama of Number Theory or The View from Baker's Garden

$124.00 (C)

G. Wüstholz, Kunrun Yui, Sinnou David, Noriko Hirata-Kohno, Kálmán Györy, Yuri F. Bilu, Paula B. Cohen, Gisbert Wüstholz, Jürgen Wolfart, Peter Sarnak, Dorian Goldfeld, Yu. V. Nesterenko, Eva Bayer-Fluckiger, Tetsuji Shioda, Enrico Bombieri, Jan-Hendrik Evertse, G. Faltings, D. W. Masser, V. V. Beresnevich, V. I. Bernik, M. M. Dodson, Gregory Margulis, Ming-Chit Liu, Tianze Wang, T. N. Shorey, A. Schinzel, D. R. Heath-Brown
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  • Date Published: October 2002
  • availability: Available
  • format: Hardback
  • isbn: 9780521807999

$ 124.00 (C)
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About the Authors
  • Alan Baker's 60th birthday in August 1999 offered an ideal opportunity to organize a conference at ETH Zurich with the goal of presenting the state of the art in number theory and geometry. Many of the leaders in the subject were brought together to present an account of research in the last century as well as speculations for possible further research. The papers in this volume cover a broad spectrum of number theory including geometric, algebrao-geometric and analytic aspects. This volume will appeal to number theorists, algebraic geometers, and geometers with a number theoretic background. However, it will also be valuable for mathematicians (in particular research students) who are interested in being informed in the state of number theory at the start of the 21st century and in possible developments for the future.

    • Papers on a broad spectrum of number theory
    • All contributors were high quality invited speakers
    • Perspectives on research in the twenty-first century
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    Product details

    • Date Published: October 2002
    • format: Hardback
    • isbn: 9780521807999
    • length: 374 pages
    • dimensions: 231 x 155 x 23 mm
    • weight: 0.67kg
    • contains: 1 b/w illus. 3 tables
    • availability: Available
  • Table of Contents

    Introduction
    1. One century of logarithmic forms G. Wüstholz
    2. Report on p-adic logarithmic forms Kunrun Yui
    3. Recent progress on linear forms in elliptic logarithms Sinnou David and Noriko Hirata-Kohno
    4. Solving Diophantine equations by Baker's theory Kálmán Györy
    5. Baker's method and modular curves Yuri F. Bilu
    6. Application of the André–Oort conjecture Paula B. Cohen and Gisbert Wüstholz
    7. Regular dessins Jürgen Wolfart
    8. Maass cusp forms with integer coefficients Peter Sarnak
    9. Modular forms, elliptic curves and the ABC-conjecture Dorian Goldfeld
    10. On the algebraic independence of numbers Yu. V. Nesterenko
    11. Ideal lattices Eva Bayer-Fluckiger
    12. Integral points and Mordell–Weil lattices Tetsuji Shioda
    13. Forty years of effective results in Diophantine theory Enrico Bombieri
    14. Points on subvarieties of tori Jan-Hendrik Evertse
    15. A new application of Diophantine approximations G. Faltings
    16. Search bounds for Diophantine equations D. W. Masser
    17. Regular systems and ubiquity V. V. Beresnevich, V. I. Bernik and M. M. Dodson
    18. Diophantine approximation, lattices and flows Gregory Margulis
    19. Baker's constant and Vinogradov's bound Ming-Chit Liu and Tianze Wang
    20. Powers in arithmetic progression T. N. Shorey
    21. Greatest common divisor A. Schinzel
    22. Heilbronn's exponential sum and transcendence theory D. R. Heath-Brown.

  • Editor

    Gisbert Wüstholz, Swiss Federal University (ETH), Zürich

    Contributors

    G. Wüstholz, Kunrun Yui, Sinnou David, Noriko Hirata-Kohno, Kálmán Györy, Yuri F. Bilu, Paula B. Cohen, Gisbert Wüstholz, Jürgen Wolfart, Peter Sarnak, Dorian Goldfeld, Yu. V. Nesterenko, Eva Bayer-Fluckiger, Tetsuji Shioda, Enrico Bombieri, Jan-Hendrik Evertse, G. Faltings, D. W. Masser, V. V. Beresnevich, V. I. Bernik, M. M. Dodson, Gregory Margulis, Ming-Chit Liu, Tianze Wang, T. N. Shorey, A. Schinzel, D. R. Heath-Brown

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