Synopses & Reviews
Graduate text/reference in number theory. Includes comprehensive reference list and 50 open problems.
Synopsis
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. Bugeaud introduces a variety of techniques which lead to many celebrated results. 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 comprehensive list of more than 600 references.
Table of Contents
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.