Discriminant equations in Diophantine number theory

Discriminant equations in Diophantine number theory

by Evertse, J. H.

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The first comprehensive and up-to-date account of discriminantequations and their applications. For graduate students and researchers.

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Title Statements

  • Full title :Discriminant equations in Diophantine number theory / Janj-HendrikEvertse, Kálmán Gyoʺry.

Summary

The first comprehensive and up-to-date account of discriminantequations and their applications. For graduate students and researchers.

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Edition Statements

  • Publication Date:2016.

Publication Statements

The Physical Object

  • Description:1 ressource en ligne

Edition Identifiers

  • ISBN:131672901X, 1316729613, 9781316729014, 9781316729618
  • oclc:on1371450961
  • LC Classification:QA242
  • Dewey Decimal:512.74

Table of Contents

Cover; Half title; Series; Title; Copyright; Contents; Preface; Acknowledgments; Summary; Part One Preliminaries; 1 Finite Étale Algebras over Fields; 1.1 Terminology for Rings and Algebras; 1.2 Finite Field Extensions; 1.3 Basic Facts on Finite Étale Algebras over Fields; 1.4 Resultants and Discriminants of Polynomials; 1.5 Characteristic Polynomial, Trace, Norm, Discriminant; 1.6 Integral Elements and Orders; 2 Dedekind Domains; 2.1 Definitions; 2.2 Ideal Theory of Dedekind Domains; 2.3 Discrete Valuations; 2.4Localization; 2.5 Integral Closure in Finite Field Extensions

2.6 Extensions of Discrete Valuations2.7 Norms of Ideals; 2.8 Discriminant and Different; 2.9 Lattices over Dedekind Domains; 2.10 Discriminants of Lattices of Étale Algebras; 3 Algebraic Number Fields; 3.1 Definitions and Basic Results; 3.1.1 Absolute Norm of an Ideal; 3.1.2 Discriminant, Class Number, Unit Group and Regulator; 3.1.3 Explicit Estimates; 3.2 Absolute Values: Generalities; 3.3 Absolute Values and Places on Number Fields; 3.4 S-integers, S-units and S-norm; 3.5 Heights and Houses; 3.6Estimates for Units and S-units

3.7 Effective Computations in Number Fields and Étale Algebras3.7.1 Algebraic Num…

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Subjects

Algebraic number theory Arithmetical algebraic geometry Diophantine equations Équations diophantiennes Géométrie algébrique arithmétique Livres numériques Théorie algébrique des nombres

Writers

Evertse, J. H. Györy, Kálmán

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