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Klappentext This is a selection of high quality articles on number theory by leading figures. Zusammenfassung This book represents the highlights of a conference hosted at ETH Zurich. It will appeal to a broad spectrum of number theorists. However! it is also for research students interested in the state of number theory at the start of the 21st century and in possible developments for the future. Inhaltsverzeichnis 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.
