A panorama in number theory or the view from Baker's garden / edited by Gisbert Wüstholz.

Format:

Book

Contributor:

Baker, Alan, 1939- editor.

Wüstholz, Gisbert, editor.

Language:

English

Subjects (All):

Number theory--Congresses.

Number theory.

Physical Description:

1 online resource (xv, 356 pages) : digital, PDF file(s).

Edition:

1st ed.

Place of Publication:

Cambridge : Cambridge University Press, 2002.

Language Note:

English

Summary:

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.

Contents:

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.

Notes:

Title from publisher's bibliographic system (viewed on 05 Oct 2015).

Includes bibliographical references.

ISBN:

1-107-13156-1

1-280-41517-7

9786610415175

0-511-17976-6

1-139-14744-7

0-511-06390-3

0-511-05757-1

0-511-33084-7

0-511-54296-8

0-511-07236-8

OCLC:

776979059