Distribution Modulo One and Diophantine Approximation

By: Yann Bugeaud

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Hardcover | 5 July 2012

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Hardcover
318 Pages

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22.86 x 15.24 x 2.24

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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.

Industry Reviews

"The reader may learn a lot from this book about various techniques used i this subject over many years (e.g., classical and metrical Diophantine approximation, combinatorics on words) and, in addition, find the proofs of some very recent results." - Arturas Dubickas, Mathematical Reviews

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Distribution modulo one
On the fractional parts of powers of real numbers
On the fractional parts of powers of algebraic numbers
Normal numbers
Further explicit constructions of normal and non-normal numbers
Normality to different bases
Diophantine approximation and digital properties
Digital expansion of algebraic numbers
Continued fraction expansions and beta-expansions
Conjectures and open problems
Combinatorics on words
Some elementary lemmata
Measure theory
Continued fractions
Diophantine approximation
Recurrence sequences
References
Index
Table of Contents provided by Publisher. All Rights Reserved.

Distribution Modulo One and Diophantine Approximation

At a Glance

Hardcover

Industry Reviews

Shipping

How to return your order

Defective items

You Can Find This Book In

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