Distribution modulo one and diophantine approximation
 Author/Creator
 Bugeaud, Yann, 1971
 Language
 English.
 Imprint
 Cambridge, UK ; New York : Cambridge University Press, 2012.
 Physical description
 xvi, 300 p. : ill ; 24 cm.
 Series
 Cambridge tracts in mathematics ; 193.
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Available online
 dx.doi.org Cambridge Books Online
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QA242 .B84 2012

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QA242 .B84 2012
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Contents/Summary
 Bibliography
 Includes bibliographical references (p. 257298) and index.
 Contents

 1. Distribution modulo one 2. On the fractional parts of powers of real numbers 3. On the fractional parts of powers of algebraic numbers 4. Normal numbers 5. Further explicit constructions of normal and nonnormal numbers 6. Normality to different bases 7. Diophantine approximation and digital properties 8. Digital expansion of algebraic numbers 9. Continued fraction expansions and betaexpansions 10. Conjectures and open problems A. Combinatorics on words B. Some elementary lemmata C. Measure theory D. Continued fractions E. Diophantine approximation F. Recurrence sequences References Index.
 (source: Nielsen Book Data)
 Publisher's Summary
 This book presents stateoftheart 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 nonexperts. Specialists will appreciate the inclusion of over 50 open problems and the rich and comprehensive bibliography of over 700 references.
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Bibliographic information
 Publication date
 2012
 Responsibility
 Yann Bugeaud.
 Series
 Cambridge tracts in mathematics ; 193
 ISBN
 9780521111690 (hardback)
 0521111692 (hardback)