Applications of Diophantine Approximation to Integral Points and Transcendence

Introduction to Diophantine approximation and equations focusing on Schmidt's subspace theorem, with applications to transcendence.

Pietro Corvaja (Author), Umberto Zannier (Author)

9781108424943, Cambridge University Press

Hardback, published 3 May 2018

208 pages, 2 b/w illus. 100 exercises
23.5 x 15.7 x 1.5 cm, 0.4 kg

'Researchers new to Diophantine approximation and experts alike will find this volume to be an essential account of this time-honored subject.' Matthew A. Papanikolas, MathsSciNet

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.

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.

Subject Areas: Algebraic geometry [PBMW], Analytic geometry [PBMS], Number theory [PBH]