ENGLISH

Linear Forms in Logarithms and Applications

By Yann Bugeaud

Book information

Publisher
Euopean Mathematical Society
Year
2018
ISBN
9783037191835
Language
english
Format
PDF
Filesize
1 MB (1459772 bytes)
Series
IRMA Lectures in Mathematics and Theoretical Physics
Pages
242\242
Time added
2018-02-09 17:06:52

Description

The aim of this book is to serve as an introductory text to the theory of linear forms in the logarithms of algebraic numbers, with a special emphasis on a large variety of its applications. We wish to help students and researchers to learn what is hidden inside the blackbox ‚Baker's theory of linear forms in logarithms' (in complex or in p-adic logarithms) and how this theory applies to many Diophantine problems, including the effective resolution of Diophantine equations, the abc -conjecture, and upper bounds for the irrationality measure of some real numbers. Written for a broad audience, this accessible and self-contained book can be used for graduate courses (some 30 exercises are supplied). Specialists will appreciate the inclusion of over 30 open problems and the rich bibliography of over 450 references. Keywords: Baker's theory, linear form in logarithms, Diophantine equation, Thue equation, abc -conjecture, primitive divisor, irrationality measure, p-adic analysis

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