Effective Results and Methods for Diophantine Equations over Finitely Generated Domains

Kálmán Győry author Jan-Hendrik Evertse author

Format:Paperback

Publisher:Cambridge University Press

Published:28th Apr '22

Should be back in stock very soon

Effective Results and Methods for Diophantine Equations over Finitely Generated Domains cover

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

This book provides a comprehensive guide to Diophantine equations over finitely generated domains, with a focus on proving effective finiteness results. No specialized knowledge is required, enabling graduate students and experts alike to learn the necessary techniques and apply them in their own research.This book provides the first thorough treatment of effective results and methods for Diophantine equations over finitely generated domains. Compiling diverse results and techniques from papers written in recent decades, the text includes an in-depth analysis of classical equations including unit equations, Thue equations, hyper- and superelliptic equations, the Catalan equation, discriminant equations and decomposable form equations. The majority of results are proved in a quantitative form, giving effective bounds on the sizes of the solutions. The necessary techniques from Diophantine approximation and commutative algebra are all explained in detail without requiring any specialized knowledge on the topic, enabling readers from beginning graduate students to experts to prove effective finiteness results for various further classes of Diophantine equations.

'… I found the book to be presented and structured very well. It covers the topics and results that one would expect and hope to find in a book on this subject, as well as the new results mentioned above. But as the authors state towards the end of their preface, more possibilities exist for the application of their techniques. The authors have certainly done a good job of writing a clear, accessible account of this subject that should help to fulfill their hope that others will continue their work.' Paul M. Voutier, MathSciNet

ISBN: 9781009005852

Dimensions: 230mm x 152mm x 13mm

Weight: 360g

240 pages