Effective Results and Methods for Diophantine Equations over Finitely Generated Domains

by Jan-Hendrik Evertse , Kalman Gyory

Book Details

Format Paperback / Softback

Book Series London Mathematical Society Lecture Note Series

ISBN-10 1009005855

ISBN-13 9781009005852

Publisher Cambridge University Press

Imprint Cambridge University Press

Country of Manufacture GB

Country of Publication GB

Publication Date Apr 28th, 2022

Print length 240 Pages

Weight 376 grams

Dimensions 15.30 x 22.90 x 1.80 cms

Product Classification: Algebra Number theory Algebraic geometry

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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.

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