Unit Equations in Diophantine Number Theory (Hardcover)

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.