Distribution Modulo One and Diophantine Approximation (Cambridge Tracts in Mathematics)

Bugeaud, Professor Yann

ISBN 10: 0521111692 / ISBN 13: 9780521111690

Published by Cambridge University Press, 2012

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Bibliographic Details

• Title: Distribution Modulo One and Diophantine Approximation (Cambridge Tracts in Mathematics)
• Publisher: Cambridge University Press
• Publication Date: 2012
• Language: English
• ISBN 10: 0521111692
• ISBN 13: 9780521111690
• Binding: Hardcover
• Condition: Like New
• Book Type: book

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Synopsis

This book presents state-of-the-art research on the distribution modulo one of sequences of integral powers of real numbers and related topics. Most of the results have never before appeared in one book and many of them were proved only during the last decade. Topics covered include the distribution modulo one of the integral powers of 3/2 and the frequency of occurrence of each digit in the decimal expansion of the square root of two. The author takes a point of view from combinatorics on words and introduces a variety of techniques, including explicit constructions of normal numbers, Schmidt's games, Riesz product measures and transcendence results. With numerous exercises, the book is ideal for graduate courses on Diophantine approximation or as an introduction to distribution modulo one for non-experts. Specialists will appreciate the inclusion of over 50 open problems and the rich and comprehensive bibliography of over 700 references.

About the Author

Yann Bugeaud is a Professor in the Institut de Recherche Mathématique Avancée (IRMA) at the University of Strasbourg, France.