To help the reader access the current state of research in this branch of number theory, Yann Bugeaud combines the most important results previously scattered throughout the research literature and also includes a number of significant open questions. Although written for graduates who wish to pursue research, the collection will also be an invaluable reference work for established researchers.
'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
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.