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

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Gisbert Wüstholz
Cambridge University Press, Sep 26, 2002 - Mathematics - 356 pages
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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.
 

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Contents

One Century of Logarithmic Forms G Wiistholz
1
Report on padic Logarithmic Forms Kunrui Yu
11
Recent Progress on Linear Forms in Elliptic Logarithms Sinnou David Noriko HirataKohno
26
Sinnou David Universite P et M Curie Paris VI Institut Mathematique
36
Solving Diophantine Equations by Bakers Theory Kdlmdn Gyory
38
Bakers Method and Modular Curves Yuri F Bilu
73
Application of the AndreOort Conjecture to some Questions in Transcendence Paula B Cohen Gisbert Wiistholz
89
G Wiistholz ETH Zurich ETH Zentrum DMATH HG G 66 3 Raemistrasse
101
Ideal Lattices Eva BayerFluckiger
168
Integral Points and MordellWeil Lattices Tetsuji Shioda
185
Forty Years of Effective Results in Diophantine Theory Enrico Bombieri
194
Points on Subvarieties of Tori JanHendrik Evertse
214
A New Application of Diophantine Approximations G Faltings
231
Search Bounds for Diophantine Equations D W Masser
247
Regular Systems Ubiquity and Diophantine Approximation V V Beresnevich V I Bernik MM Dodson
260
Diophantine Approximation Lattices and Flows on Homogeneous Spaces Gregory Margulis
280

Regular Dessins Endomorphisms of Jacobians and Transcendence Jurgen Wolfart
107
Maass Cusp Forms with Integer Coefficients Peter Sarnak
121
Modular Forms Elliptic Curves and the ABCConjecture Dorian Goldfeld
128
JanHendrik Evertse Universiteit Leiden Mathematisch Instituut Postbus
147
On the Algebraic Independence of Numbers Yu V Nesterenko
148
On Linear Ternary Equations with Prime Variables Bakers Constant
311
Powers in Arithmetic Progression T N Shorey
325
On the Greatest Common Divisor of Two Univariate Polynomials I
337
Heilbronns Exponential Sum and Transcendence Theory
353
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