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

This is a selection of high quality articles on number theory by leading figures.

Gisbert Wüstholz (Edited by)

9780521807999, Cambridge University Press

Hardback, published 26 September 2002

374 pages, 1 b/w illus. 3 tables
23.1 x 15.5 x 2.3 cm, 0.67 kg

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 would like to be informed of the state of number theory at the start of the 21st century and in possible developments for the future.

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.

Subject Areas: Number theory [PBH]