A panorama in number theory or the view from Baker's garden [E-Book] / edited by Gisbert Wüstholz.
Baker, Alan, (editor)
Wüstholz, Gisbert, (editor)
Cambridge : Cambridge University Press, 2002
1 online resource (xv, 356 pages)
Full Text
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505 0 |a One century of logarithmic forms / G. Wüstholz -- Report on p-adic logarithmic forms / Kunrui Yu -- Recent progress on linear forms in elliptic logarithms / Sinnou David & Noriko Hirata-Kohno -- Solving diophantine equations by Baker's theory / Kálmán Győry -- Baker's method and modular curves / Yuri F. Bilu -- Application of the Andrè-Oort conjecture to some questions in transcendence / Paula B. Cohen & Gilbert Wüstholz -- Regular dessins, endomorphisms of Jacobians, and transcendence / Jürgen Wolfart -- Maass cusp forms with integer coefficients / Peter Sarnak -- Modular forms, elliptic curves and the ABC-conjecture / Dorian Goldfeld -- On the algebraic independence of numbers / Yu. V. Nesterenko -- Ideal lattices / Eva Bayer-Fluckiger -- Integral points and Mordell-Weil lattices / Tetsuji Shioda -- Forty years of effective results in diophantine theory / Enrico Bombieri -- Points on subvarieties of Tori / Jan-Hendrik Evertse -- A new application of diophantine approximations / G. Faltings -- Search bounds for diophantine equations / D.W. Masser -- Regular systems, ubiquity and diophantine approximation / V.V. Beresnevich, V.I. Bernik & M.M. Dodson -- Diophantine approximation, lattices and flows on homogeneous spaces / Gregory Margulis -- On linear ternary equations with prime variables / Ming-Chit Liu & Tianze Wang -- Powers in arithmetic progression / T.N. Shorey -- On the greatest common divisor of two univariate polynomials / A. Schinzel -- Heilbronn's exponential sum and transcendence theory / D.R. Heath-Brown. 
520 |a 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. 
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