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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.
| Clasificación: | Libro Electrónico |
|---|---|
| Autores principales: | , |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Cambridge, UK :
Cambridge University Press,
2016.
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| Temas: | |
| Acceso en línea: | Texto completo |
MARC
| LEADER | 00000cam a2200000 i 4500 | ||
|---|---|---|---|
| 001 | EBSCO_ocn960643263 | ||
| 003 | OCoLC | ||
| 005 | 20231017213018.0 | ||
| 006 | m o d | ||
| 007 | cr cnu---unuuu | ||
| 008 | 161013s2016 enk ob 001 0 eng d | ||
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| 020 | |a 9781316729618 |q (electronic bk.) | ||
| 020 | |a 1316729613 |q (electronic bk.) | ||
| 020 | |a 9781316729014 |q (electronic bk.) | ||
| 020 | |a 131672901X |q (electronic bk.) | ||
| 020 | |z 1107097614 | ||
| 020 | |z 9781107097612 | ||
| 029 | 1 | |a AU@ |b 000059028675 | |
| 035 | |a (OCoLC)960643263 |z (OCoLC)960737779 |z (OCoLC)960834934 |z (OCoLC)960838090 |z (OCoLC)961818180 |z (OCoLC)961828500 |z (OCoLC)962257607 |z (OCoLC)962442750 |z (OCoLC)962786862 |z (OCoLC)962805530 |z (OCoLC)964333354 |z (OCoLC)965147676 |z (OCoLC)966891334 | ||
| 050 | 4 | |a QA242 | |
| 072 | 7 | |a MAT |x 002040 |2 bisacsh | |
| 082 | 0 | 4 | |a 512.74 |2 23 |
| 049 | |a UAMI | ||
| 100 | 1 | |a Evertse, J. H., |e author. | |
| 245 | 1 | 0 | |a Discriminant equations in Diophantine number theory / |c Janj-Hendrik Evertse, Kálmán Gyoʺry. |
| 264 | 1 | |a Cambridge, UK : |b Cambridge University Press, |c 2016. | |
| 300 | |a 1 online resource | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 504 | |a Includes bibliographical references and index. | ||
| 588 | 0 | |a Print version record. | |
| 505 | 0 | |a 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 | |
| 505 | 8 | |a 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 | |
| 505 | 8 | |a 3.7 Effective Computations in Number Fields and Étale Algebras3.7.1 Algebraic Number Fields; 3.7.2 Relative Extensions and Finite Étale Algebras; 4 Tools from the Theory of Unit Equations; 4.1 Effective Results over Number Fields; 4.1.1 Equations in Units of Rings of Integers; 4.1.2 Equations with Unknowns from a Finitely Generated Multiplicative Group; 4.2 Effective Results over Finitely Generated Domains; 4.3 Ineffective Results, Bounds for the Number of Solutions; Part Two Monic Polynomials and Integral Elements of Given Discriminant, Monogenic Orders; 5 Basic Finiteness Theorems | |
| 505 | 8 | |a 5.1 Basic Facts on Finitely Generated Domains5.2 Discriminant Forms and Index Forms; 5.3 Monogenic Orders, Power Bases, Indices; 5.4 Finiteness Results; 5.4.1 Discriminant Equations for Monic Polynomials; 5.4.2 Discriminant Equations for Integral Elements in Étale Algebras; 5.4.3 Discriminant Form and Index Form Equations; 5.4.4 Consequences for Monogenic Orders; 6 Effective Results over Z; 6.1 Discriminant Form and Index Form Equations; 6.2 Applications to Integers in a Number Field; 6.3 Proofs; 6.4 Algebraic Integers of Arbitrary Degree; 6.5 Proofs | |
| 505 | 8 | |a 6.6 Monic Polynomials of Given Discriminant6.7 Proofs; 6.8 Notes; 6.8.1 Some Related Results; 6.8.2 Generalizations over Z; 6.8.3 Other Applications; 7 Algorithmic Resolution of Discriminant Form and Index Form Equations; 7.1 Solving Discriminant Form and Index Form Equations via Unit Equations, A General Approach; 7.1.1 Quintic Number Fields; 7.1.2 Examples; 7.2 Solving Discriminant Form and Index Form Equations via Thue Equations; 7.2.1 Cubic Number Fields; 7.2.2 Quartic Number Fields; 7.2.3 Examples; 7.3 The Solvability of Index Equations in Various Special Number Fields; 7.4 Notes | |
| 520 | |a The first comprehensive and up-to-date account of discriminant equations and their applications. For graduate students and researchers. | ||
| 590 | |a eBooks on EBSCOhost |b EBSCO eBook Subscription Academic Collection - Worldwide | ||
| 650 | 0 | |a Diophantine equations. | |
| 650 | 0 | |a Algebraic number theory. | |
| 650 | 0 | |a Arithmetical algebraic geometry. | |
| 650 | 6 | |a Équations diophantiennes. | |
| 650 | 6 | |a Théorie algébrique des nombres. | |
| 650 | 6 | |a Géométrie algébrique arithmétique. | |
| 650 | 7 | |a MATHEMATICS |x Algebra |x Intermediate. |2 bisacsh | |
| 650 | 7 | |a Algebraic number theory |2 fast | |
| 650 | 7 | |a Arithmetical algebraic geometry |2 fast | |
| 650 | 7 | |a Diophantine equations |2 fast | |
| 700 | 1 | |a Györy, Kálmán, |e author. | |
| 776 | 0 | 8 | |i Print version: |a Evertse, Jan-Hendrik. |t Discriminant equations in diophantine number theory. |d [Place of publication not identified] : Cambridge Univ Press, 2016 |z 1107097614 |w (OCoLC)944462906 |
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