Effective Results and Methods for Diophantine Equations over Finitely Generated Domains
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:
AlgebraNumber theoryAlgebraic geometry
Ksh 10,450.00
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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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