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  3. Distribution Modulo One and Diophantine Approximation
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    • Publisher:
      Cambridge University Press
      Publication date:
      05 October 2012
      05 July 2012
      ISBN:
      9781139017732
      9780521111690
      DOI:
      https://doi.org/10.1017/CBO9781139017732
      Dimensions:
      (228 x 152 mm)
      Weight & Pages:
      0.59kg, 316 Pages
      Dimensions:
      Weight & Pages:
      • Subjects:
      Mathematics (general), Mathematics, Number Theory
      Series:
      Cambridge Tracts in Mathematics (193)
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    Subjects:
    Mathematics (general), Mathematics, Number Theory
    Series:
    Cambridge Tracts in Mathematics (193)
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    Book description

    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.

    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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