Discriminant equations in Diophantine number theory
The first comprehensive and up-to-date account of discriminant equations and their applications. For graduate students and researchers.
Read More ↓Title Statements
- Full title :Discriminant equations in Diophantine number theory / Janj-Hendrik Evertse, Kálmán Győry.
Summary
The first comprehensive and up-to-date account of discriminant equations and their applications. For graduate students and researchers.
Read More ↓Edition Statements
- Publication Date:2017.
Publication Statements
- Publisher(s):Cambridge University Press
- Place of Publication:Cambridge, UK
- Language:eng
- Publication Date:2017.
The Physical Object
- Description:1 online resource
Edition Identifiers
- ISBN:9781316729014, 9781316729618, 1316729613, 131672901X
- oclc:ocn963352208
- LC Classification:QA242 INTERNET
- 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; 2.4 Localization; 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; 3.6 Estimates for Units and S-units.
3.7 Effective Computations in Number Fields and Étale Algebras3.7.1 Algebraic…
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