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.
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.
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.
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