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Approximation by Algebraic Numbers : Cambridge Tracts in Mathematics - Yann Bugeaud

Approximation by Algebraic Numbers

Cambridge Tracts in Mathematics


Published: 20th December 2007
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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.

'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.' Bulletin of the London Mathematical Society

Frequently used notation
Approximation by rational numbers
Approximation to algebraic numbers
The classifications of Mahler and Koksma
Mahler-s Conjecture on S-numbers
Hausdorff dimension of exceptional sets
Deeper results on the measure of exceptional sets
On T-numbers and U-numbers
Other classifications of real and complex numbers
Approximation in other fields
Conjectures and open questions
Lemmas on polynomials
Geometry of numbers
Table of Contents provided by Publisher. All Rights Reserved.

ISBN: 9780521045674
ISBN-10: 0521045673
Series: Cambridge Tracts in Mathematics
Audience: Professional
Format: Paperback
Language: English
Number Of Pages: 292
Published: 20th December 2007
Publisher: Cambridge University Press
Country of Publication: GB
Dimensions (cm): 22.8 x 15.2  x 1.7
Weight (kg): 0.43