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.
Pietro Corvaja is Full Professor of Geometry at the Universita degli Studi di Udine, Italy. His research interests include arithmetic geometry, Diophantine approximation and the theory of transcendental numbers. Umberto Zannier is Full Professor of Geometry at Scuola Normale Superiore, Pisa. His research interests include number theory, especially Diophantine geometry and related topics.
Reviews for Applications of Diophantine Approximation to Integral Points and Transcendence
'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