Jan-Hendrik Evertse works in the Mathematical Institute at Leiden University. His research concentrates on Diophantine approximation and applications to Diophantine problems. In this area he has obtained some influential results, in particular on estimates for the numbers of solutions of Diophantine equations and inequalities.
Inhaltsangabe
Preface Summary Part I. Preliminaries: 1. Finite étale algebras over fields 2. Dedekind domains 3. Algebraic number fields 4. Tools from the theory of unit equations Part II. Monic Polynomials and Integral Elements of Given Discriminant, Monogenic Orders: 5. Basic finiteness theorems 6. Effective results over Z 7. Algorithmic resolution of discriminant form and index form equations 8. Effective results over the S-integers of a number field 9. The number of solutions of discriminant equations 10. Effective results over finitely generated domains 11. Further applications Part III. Binary Forms of Given Discriminant: 12. A brief overview of the basic finiteness theorems 13. Reduction theory of binary forms 14. Effective results for binary forms of given discriminant 15. Semi-effective results for binary forms of given discriminant 16. Invariant orders of binary forms 17. On the number of equivalence classes of binary forms of given discriminant 18. Further applications Glossary of frequently used notation References Index.
Preface Summary Part I. Preliminaries: 1. Finite étale algebras over fields 2. Dedekind domains 3. Algebraic number fields 4. Tools from the theory of unit equations Part II. Monic Polynomials and Integral Elements of Given Discriminant, Monogenic Orders: 5. Basic finiteness theorems 6. Effective results over Z 7. Algorithmic resolution of discriminant form and index form equations 8. Effective results over the S-integers of a number field 9. The number of solutions of discriminant equations 10. Effective results over finitely generated domains 11. Further applications Part III. Binary Forms of Given Discriminant: 12. A brief overview of the basic finiteness theorems 13. Reduction theory of binary forms 14. Effective results for binary forms of given discriminant 15. Semi-effective results for binary forms of given discriminant 16. Invariant orders of binary forms 17. On the number of equivalence classes of binary forms of given discriminant 18. Further applications Glossary of frequently used notation References Index.
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