Effective Results and Methods for Diophantine Equations over Finitely Generated Domains

Cambridge University Press eBooks

Abstract

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.

Authors 2

1. Jan‐Hendrik Evertse Aachen

   Leiden University

   Affiliation as printed

   Universiteit Leiden

2. Kálmán Győry

   University of Debrecen

   Affiliation as printed

   Debreceni Egyetem, Hungary