Approximation by algebraic numbers
Author(s)
Bibliographic Information
Approximation by algebraic numbers
（Cambridge tracts in mathematics, 160）
Cambridge University Press, 2004
- : hbk
Available at / 36 libraries
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Hokkaido University, Library, Graduate School of Science, Faculty of Science and School of Science図書
DC22:512.74/B8652080018285
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Note
Includes bibliographical references (p. 240-272) and index
Description and Table of Contents
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.
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.
by "Nielsen BookData"
