Jan-Hendrik Evertse is Assistant Professor 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. He has written more than 75 research papers and co-authored one book with Bas Edixhoven entitled Diophantine Approximation and Abelian Varieties (2003).
Preface
Summary
Glossary of frequently used notation
Part I. Preliminaries: 1. Basic algebraic number theory
2. Algebraic function fields
3. Tools from Diophantine approximation and transcendence theory
Part II. Unit equations and applications: 4. Effective results for unit equations in two unknowns over number fields
5. Algorithmic resolution of unit equations in two unknowns
6. Unit equations in several unknowns
7. Analogues over function fields
8. Effective results for unit equations over finitely generated domains
9. Decomposable form equations
10. Further applications
References
Index.
