![Solving Elliptic Diophantine Equations by Estimating Linaer [i.e. Linear] Forms in Elliptic Logarithms PDF](https://books.google.com/books/content/images/frontcover/t9eIHAAACAAJ?fife=w150-h200)
Author: R. J. StroekerPublisher:
ISBN:
Category :
Languages : en
Pages : 20
Book Description
Solving Elliptic Diophantine Equations by Estimating Linaer [i.e. Linear] Forms in Elliptic Logarithms
![Solving Elliptic Diophantine Equations by Estimating Linaer [i.e. Linear] Forms in Elliptic Logarithms PDF](https://books.google.com/books/content/images/frontcover/t9eIHAAACAAJ?fife=w80-h100)
Author: R. J. StroekerElliptic Diophantine Equations
Author: Nikos TzanakisPublisher: Walter de Gruyter
ISBN: 3110281147
Category : Mathematics
Languages : en
Pages : 196
Book 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.
Elliptic Diophantine Equations: A Concrete Approach Via the Elliptic Logarithm
Author: Nikolaos G. ; Tzanakis Tzanakis (Nikos)Publisher:
ISBN: 9783110281156
Category :
Languages : en
Pages : 195
Book Description
On the Elliptic Logarithm Method for Elliptic Diophantine Equations
Author: R. J. StroekerLinear Forms in the Logarithms of Three Or Four Algebraic Numbers with an Application to Solving Diophantine Equations
Author: Lisa K. ElderbrockPublisher:
ISBN:
Category : Diophantine equations
Languages : en
Pages : 384
Book Description
Exponential Diophantine Equations
Author: T. N. ShoreyPublisher: Cambridge University Press
ISBN: 9780521268264
Category : Mathematics
Languages : en
Pages : 256
Book Description
This is a integrated presentation of the theory of exponential diophantine equations. The authors present, in a clear and unified fashion, applications to exponential diophantine equations and linear recurrence sequences of the Gelfond-Baker theory of linear forms in logarithms of algebraic numbers. Topics covered include the Thue equations, the generalised hyperelliptic equation, and the Fermat and Catalan equations. The necessary preliminaries are given in the first three chapters. Each chapter ends with a section giving details of related results.