Approximation by Algebraic Numbers
By (author) Yann Bugeaud
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Approximation by Algebraic Numbers by Yann Bugeaud
Book DescriptionAlgebraic 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.
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Book DetailsISBN: 9780521045674
(228mm x 152mm x 17mm)
Imprint: Cambridge University Press
Publisher: Cambridge University Press
Publish Date: 3-Dec-2007
Country of Publication: United Kingdom
Books By Author Yann Bugeaud
Distribution Modulo One and Diophantine Approximation, Hardback (July 2012)
A treatment of cutting-edge research on the distribution modulo one of sequences and related topics, with exercises and open problems.
Approximation by Algebraic Numbers, Hardback (November 2004)» View all books by Yann Bugeaud
Graduate text/reference in number theory. Includes comprehensive reference list and 50 open problems.
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