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

ISBN-13: 9780521807999 / Angielski / Twarda / 2002 / 374 str.

Wüstholz, Gisbert

Opis

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.

Spis treści

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.