Elliptic Diophantine Equations : A Concrete Approach Via the Elliptic Logarithm
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| Title: | Elliptic Diophantine Equations : A Concrete Approach Via the Elliptic Logarithm |
|---|---|
| Description: | This book presents in a unified and concrete way the beautiful and deep mathematics - both theoretical and computational - on which the explicit solution of an elliptic Diophantine equation is based. It collects numerous results and methods that are scattered in the literature. Some results are hidden behind a number of routines in software packages, like Magma and Maple; professional mathematicians very often use these routines just as a black-box, having little idea about the mathematical treasure behind them. Almost 20 years have passed since the first publications on the explicit solution of elliptic Diophantine equations with the use of elliptic logarithms. The'art'of solving this type of equation has now reached its full maturity. The author is one of the main persons that contributed to the development of this art. The monograph presents a well-balanced combination of a variety of theoretical tools (from Diophantine geometry, algebraic number theory, theory of linear forms in logarithms of various forms - real/complex and p-adic elliptic - and classical complex analysis), clever computational methods and techniques (LLL algorithm and de Weger's reduction technique, AGM algorithm, Zagier's technique for computing elliptic integrals), ready-to-use computer packages. A result is the solution in practice of a large general class of Diophantine equations. |
| Authors: | Nikos Tzanakis |
| Resource Type: | eBook. |
| Subjects: | Elliptic functions, Diophantine equations |
| Categories: | MATHEMATICS / Algebra / Abstract, MATHEMATICS / Geometry / Algebraic, MATHEMATICS / Number Theory, MATHEMATICS / Reference, MATHEMATICS / Research |
| Database: | eBook Collection (EBSCOhost) |
| FullText | Links: – Type: ebook-pdf Text: Availability: 0 |
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| Header | DbId: nlebk DbLabel: eBook Collection (EBSCOhost) An: 641752 RelevancyScore: 1051 AccessLevel: 6 PubType: eBook PubTypeId: ebook PreciseRelevancyScore: 1050.81640625 |
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| RecordInfo | BibRecord: BibEntity: Classifications: – Code: 512.72 Scheme: ddc Type: prePub Languages: – Code: eng Text: English Subjects: – SubjectFull: Elliptic functions Type: general – SubjectFull: Diophantine equations Type: general Titles: – TitleFull: Elliptic Diophantine Equations : A Concrete Approach Via the Elliptic Logarithm Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Nikos Tzanakis – PersonEntity: Name: NameFull: Nikos Tzanakis IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 01 Type: published Y: 2013 – D: 04 M: 02 Type: profile Y: 2014 Identifiers: – Type: isbn-print Value: 9783110280913 – Type: isbn-electronic Value: 9783110281149 Numbering: – Type: volume Value: 00002 Titles: – TitleFull: Elliptic Diophantine Equations : A Concrete Approach Via the Elliptic Logarithm Type: main |
| ResultId | 1 |
