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Effective results and methods for diophantine equations over finitely

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Effective results and methods for diophantine equations over finitelyJan-Hendrik Evertse, Kálmán Győry.
作者:	Evertse, Jan-Hendrik.
其他作者:	Györy, Kálmán.
出版者:	Cambridge, United Kingdom ; New York, NY :Cambridge University Press,2022.
面頁冊數:	xxiv, 216 p. :ill., digital ;23 cm.
附註:	Title from publisher's bibliographic system (viewed on 31 Aug 2022).
標題:	Diophantine equations.
電子資源:	https://doi.org/10.1017/9781009042109
ISBN:	9781009042109

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

Effective results and methods for diophantine equations over finitely[electronic resource] /Jan-Hendrik Evertse, Kálmán Győry. - Cambridge, United Kingdom ; New York, NY :Cambridge University Press,2022. - xxiv, 216 p. :ill., digital ;23 cm. - London Mathematical Society lecture note series ;475. - London Mathematical Society lecture note series ;353..

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

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.

ISBN: 9781009042109Subjects--Topical Terms:

387265
Diophantine equations.

LC Class. No.: QA242 / .E939 2022

Dewey Class. No.: 512.72

Effective results and methods for diophantine equations over finitely
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520 $a 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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