Discriminant Equations in Diophantine Number Theory

Nonfiction, Science & Nature, Mathematics, Number Theory, Geometry
Cover of the book Discriminant Equations in Diophantine Number Theory by Jan-Hendrik Evertse, Kálmán Győry, Cambridge University Press
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Author: Jan-Hendrik Evertse, Kálmán Győry ISBN: 9781316727218
Publisher: Cambridge University Press Publication: November 3, 2016
Imprint: Cambridge University Press Language: English
Author: Jan-Hendrik Evertse, Kálmán Győry
ISBN: 9781316727218
Publisher: Cambridge University Press
Publication: November 3, 2016
Imprint: Cambridge University Press
Language: English

Discriminant equations are an important class of Diophantine equations with close ties to algebraic number theory, Diophantine approximation and Diophantine geometry. This book is the first comprehensive account of discriminant equations and their applications. It brings together many aspects, including effective results over number fields, effective results over finitely generated domains, estimates on the number of solutions, applications to algebraic integers of given discriminant, power integral bases, canonical number systems, root separation of polynomials and reduction of hyperelliptic curves. The authors' previous title, Unit Equations in Diophantine Number Theory, laid the groundwork by presenting important results that are used as tools in the present book. This material is briefly summarized in the introductory chapters along with the necessary basic algebra and algebraic number theory, making the book accessible to experts and young researchers alike.

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Discriminant equations are an important class of Diophantine equations with close ties to algebraic number theory, Diophantine approximation and Diophantine geometry. This book is the first comprehensive account of discriminant equations and their applications. It brings together many aspects, including effective results over number fields, effective results over finitely generated domains, estimates on the number of solutions, applications to algebraic integers of given discriminant, power integral bases, canonical number systems, root separation of polynomials and reduction of hyperelliptic curves. The authors' previous title, Unit Equations in Diophantine Number Theory, laid the groundwork by presenting important results that are used as tools in the present book. This material is briefly summarized in the introductory chapters along with the necessary basic algebra and algebraic number theory, making the book accessible to experts and young researchers alike.

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