Unit Equations in Diophantine Number Theory

ISBN-13: 9781107097605 / Angielski / Twarda / 2015 / 378 str.

Jan-Hendrik Evertse; Kalman Gy Ry

Opis

A comprehensive, graduate-level treatment of unit equations and their various applications.

Recenzje

'Understanding the book requires only basic knowledge in algebra (groups, commutative rings, fields, Galois theory and elementary algebraic number theory). In particular the concepts of height, places and valuations play an important role. … In addition to providing a survey, the authors improve both formulations and proofs of various important existing results in the literature, making their book a valuable asset for researchers in this area. … I thank them for their fast and clear answers.' Pieter Moree, Nieuw Archief voor Wiskunde

Spis treści

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.