eBook - PDF

Elliptic Diophantine Equations

Name: Elliptic Diophantine Equations
ISBN: 9783110281149

A Concrete Approach via the Elliptic Logarithm

Nikos Tzanakis,

195 pages
English
PDF
Available on iOS & Android

eBook - PDF

Elliptic Diophantine Equations

A Concrete Approach via the Elliptic Logarithm

Nikos Tzanakis,

About this book

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.

Frequently asked questions

Yes, you can cancel anytime from the Subscription tab in your account settings on the Perlego website. Your subscription will stay active until the end of your current billing period. Learn how to cancel your subscription.

No, books cannot be downloaded as external files, such as PDFs, for use outside of Perlego. However, you can download books within the Perlego app for offline reading on mobile or tablet. Learn more here.

Perlego offers two plans: Essential and Complete

Essential is ideal for learners and professionals who enjoy exploring a wide range of subjects. Access the Essential Library with 800,000+ trusted titles and best-sellers across business, personal growth, and the humanities. Includes unlimited reading time and Standard Read Aloud voice.
Complete: Perfect for advanced learners and researchers needing full, unrestricted access. Unlock 1.4M+ books across hundreds of subjects, including academic and specialized titles. The Complete Plan also includes advanced features like Premium Read Aloud and Research Assistant.

Both plans are available with monthly, semester, or annual billing cycles.

We are an online textbook subscription service, where you can get access to an entire online library for less than the price of a single book per month. With over 1 million books across 1000+ topics, we’ve got you covered! Learn more here.

Look out for the read-aloud symbol on your next book to see if you can listen to it. The read-aloud tool reads text aloud for you, highlighting the text as it is being read. You can pause it, speed it up and slow it down. Learn more here.

Yes! You can use the Perlego app on both iOS or Android devices to read anytime, anywhere — even offline. Perfect for commutes or when you’re on the go.
Please note we cannot support devices running on iOS 13 and Android 7 or earlier. Learn more about using the app.

Yes, you can access Elliptic Diophantine Equations by Nikos Tzanakis in PDF and/or ePUB format, as well as other popular books in Mathematics & Abstract Algebra. We have over one million books available in our catalogue for you to explore.