Approximation by Algebraic Numbers [Paperback]

Graduate text/reference in number theory. Includes comprehensive reference list and 50 open problems.This book will enable the reader to reach the current frontier of research in this branch of number theory. It collects together all the most important results that were previously scattered through the literature as well as including a number of significant open questions. The book is written so as to be accessible to graduates who wish to pursue research in this area but will also form an invaluable reference work for established researchers.This book will enable the reader to reach the current frontier of research in this branch of number theory. It collects together all the most important results that were previously scattered through the literature as well as including a number of significant open questions. The book is written so as to be accessible to graduates who wish to pursue research in this area but will also form an invaluable reference work for established researchers.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.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.'The book is written in a relaxed style, and begins with some accessiblelóâ