Effective results and methods for diophantine equations over finitely / Jan-Hendrik Evertse, Kálmán Győry.

Format:

Book

Author/Creator:

Evertse, J. H., author.

Györy, Kálmán, author.

Series:

London Mathematical Society lecture note series ; 475.

London Mathematical Society lecture note series ; 475

Language:

English

Subjects (All):

Diophantine equations.

Number theory.

Diophantine analysis.

Physical Description:

1 online resource (xxiv, 216 pages) : digital, PDF file(s).

Place of Publication:

Cambridge, United Kingdom ; New York, NY : Cambridge University Press, 2022.

Summary:

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.

Notes:

Title from publisher's bibliographic system (viewed on 31 Aug 2022).

Includes bibliographical references and index.

Other Format:

Print version: Evertse, Jan-Hendrik Effective Results and Methods for Diophantine Equations over Finitely Generated Domains

ISBN:

1-009-04210-6

1-009-05003-6