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Approximation by Algebraic Numbers (Paperback)
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Approximation by Algebraic Numbers (Paperback)
Series: Cambridge Tracts in Mathematics
Expected to ship within 12 - 19 working days
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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.
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