Applications of Diophantine Approximation to Integral Points and Transcendence

Erscheinungsjahr 2018
ISBN: 978-1-108-42494-3
Verlag: Cambridge University Press

Buch, Englisch, Band 212, 208 Seiten, Format (B × H): 157 mm x 235 mm, Gewicht: 499 g

Reihe: Cambridge Tracts in Mathematics

This introduction to the theory of Diophantine approximation pays special regard to Schmidt's subspace theorem and to its applications to Diophantine equations and related topics. The geometric viewpoint on Diophantine equations has been adopted throughout the book. It includes a number of results, some published here for the first time in book form, and some new, as well as classical material presented in an accessible way. Graduate students and experts alike will find the book's broad approach useful for their work, and will discover new techniques and open questions to guide their research. It contains concrete examples and many exercises (ranging from the relatively simple to the much more complex), making it ideal for self-study and enabling readers to quickly grasp the essential concepts.

Autoren/Hrsg.

Corvaja, Pietro

Zannier, Umberto

Fachgebiete

• Mathematik | Informatik Mathematik Geometrie Elementare Geometrie: Allgemeines
• Mathematik | Informatik Mathematik Algebra Zahlentheorie
• Mathematik | Informatik Mathematik Geometrie Algebraische Geometrie

Inhaltsverzeichnis

Notations and conventions; Introduction; 1. Diophantine approximation and Diophantine equations; 2. Schmidt's subspace theorem and S-unit equations; 3. Integral points on curves and other varieties; 4. Diophantine equations with linear recurrences; 5. Some applications of the subspace theorem in transcendental number theory; References; Index.

Über Autor(innen)

Corvaja, Pietro
Pietro Corvaja is Full Professor of Geometry at the Universit� degli Studi di Udine, Italy. His research interests include arithmetic geometry, Diophantine approximation and the theory of transcendental numbers.

Zannier, Umberto
Umberto Zannier is Full Professor of Geometry at Scuola Normale Superiore, Pisa. His research interests include number theory, especially Diophantine geometry and related topics.