Approximation by Algebraic Numbers
1st Edition
Published on 24. January 2007
978-0-511-26202-9 (ISBN)
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 / Votes
'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 SocietyMore details
Series
Language
English
Place of publication
Cambridge
United Kingdom
Publishing group
Cambridge University Press
Target group
Professional and scholarly
Illustrations
Worked examples or Exercises; 40 Tables, color
File size
1,44 MB
ISBN-13
978-0-511-26202-9 (9780511262029)
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Schweitzer Classification
Other editions
Additional editions
Yann Bugeaud
Approximation by Algebraic Numbers
Book
12/2007
Cambridge University Press
€98.30
Shipment within 15-20 days
Yann Bugeaud
Approximation by Algebraic Numbers
Book
11/2004
Cambridge University Press
€154.10
Shipment within 15-20 days
Person
Content
Preface; Frequently used notation; 1. Approximation by rational numbers; 2. Approximation to algebraic numbers; 3. The classifications of Mahler and Koksma; 4. Mahler's conjecture on S-numbers; 5. Hausdorff dimension of exceptional sets; 6. Deeper results on the measure of exceptional sets; 7. On T-numbers and U-numbers; 8. Other classifications of real and complex numbers; 9. Approximation in other fields; 10. Conjectures and open questions; Appendix A. Lemmas on polynomials; Appendix B. Geometry of numbers; References; Index.
