Approximation by Algebraic Numbers

Yann Bugeaud

274 pages, parution le 05/11/2004

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Résumé

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.

Sommaire

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
Appendix A. Lemmas on polynomials
Appendix B. Geometry of numbers

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Caractéristiques techniques

	PAPIER
Éditeur(s)	Cambridge University Press
Auteur(s)	Yann Bugeaud
Parution	05/11/2004
Nb. de pages	274
Format	16 x 23,5
Couverture	Relié
Poids	620g
Intérieur	Noir et Blanc
EAN13	9780521823296
ISBN13	978-0-521-82329-6