Distribution modulo one and diophantine approximation

Yann Bugeaud

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.

「Nielsen BookData」より

[目次]

  • 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 non-normal numbers
  • 6. Normality to different bases
  • 7. Diophantine approximation and digital properties
  • 8. Digital expansion of algebraic numbers
  • 9. Continued fraction expansions and beta-expansions
  • 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.

「Nielsen BookData」より

この本の情報

書名 Distribution modulo one and diophantine approximation
著作者等 Bugeaud, Yann
シリーズ名 Cambridge tracts in mathematics
出版元 Cambridge University Press
刊行年月 2012
ページ数 xvi, 300 p.
大きさ 23 cm
ISBN 9780521111690
NCID BB09716851
※クリックでCiNii Booksを表示
言語 英語
出版国 イギリス
この本を: 
このエントリーをはてなブックマークに追加

このページを印刷

外部サイトで検索

この本と繋がる本を検索

ウィキペディアから連想