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Linear Forms in Logarithms and Applications
IRMA Lectures in Mathematics and Theoretical Physics Vol. 28

Yann Bugeaud (Université de Strasbourg, France)

Linear Forms in Logarithms and Applications

ISBN print 978-3-03719-183-5, ISBN online 978-3-03719-683-0
DOI 10.4171/183
February 2018, 240 pages, softcover, 17 x 24 cm.
38.00 Euro

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 e ffective 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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