Effective Results and Methods for Diophantine Equations over Finitely Generated Domains

ISBN-13: 9781009005852 / Angielski / Miękka / 2022 / 300 str.

Hungary) Gyory Kalman (Debreceni Egyetem

Opis

Provides exceptional coverage of effective solutions for Diophantine equations over finitely generated domains.

Spis treści

Preface; Glossary of frequently used notation; History and summary; 1. Ineffective results for Diophantine equations over finitely generated domains; 2. Effective results for Diophantine equations over finitely generated domains: the statements; 3. A brief explanation of our effective methods over finitely generated domains; 4. Effective results over number fields; 5. Effective results over function fields; 6. Tools from effective commutative algebra; 7. The effective specialization method; 8. Degree-height estimates; 9. Proofs of the results from Sections 2.2–2.5-use of specializations; 10. Proofs of the results from Sections 2.6–2.8-reduction to unit equations; References; Index.