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  3. Approximation by Algebraic Numbers
  • Cited by 163
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    • Publisher:
      Cambridge University Press
      Publication date:
      August 2009
      November 2004
      ISBN:
      9780511542886
      9780521823296
      9780521045674
      DOI:
      https://doi.org/10.1017/CBO9780511542886
      Dimensions:
      (228 x 152 mm)
      Weight & Pages:
      0.6kg, 292 Pages
      Dimensions:
      (228 x 152 mm)
      Weight & Pages:
      0.435kg, 292 Pages
      • Subjects:
      Mathematics (general), Mathematics, Number Theory, Discrete Mathematics Information Theory and Coding
      Series:
      Cambridge Tracts in Mathematics (160)
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    • Selected: Digital
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    Subjects:
    Mathematics (general), Mathematics, Number Theory, Discrete Mathematics Information Theory and Coding
    Series:
    Cambridge Tracts in Mathematics (160)
    Information

    Book description

    Algebraic numbers can approximate and classify any real number. Here, the author gathers together results about such approximations and classifications. Written for a broad audience, the book is accessible and self-contained, with complete and detailed proofs. Starting from continued fractions and Khintchine's theorem, Bugeaud introduces a variety of techniques, ranging from explicit constructions to metric number theory, including the theory of Hausdorff dimension. So armed, the reader is led to such celebrated advanced results as the proof of Mahler's conjecture on S-numbers, the Jarnik–Besicovitch theorem, and the existence of T-numbers. Brief consideration is given both to the p-adic and the formal power series cases. Thus the book can be used for graduate courses on Diophantine approximation (some 40 exercises are supplied), or as an introduction for non-experts. Specialists will appreciate the collection of over 50 open problems and the rich and comprehensive list of more than 600 references.

    Reviews

    'The book is written in a relaxed style, and begins with some accessible introductory chapters … It is nicely written and well explained, and proofs in the main are given in full. this book is certainly suitable for a non-expert in the area, or as a graduate course for an advanced student … All in all, this is a very nice book.'

    Source: Bulletin of the London Mathematical Society

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