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Author : J. E. Cremona
Release : 1997-05-15
Genre : Mathematics
Kind : eBook
Book Rating : 200/5 ( reviews)
Book Synopsis Algorithms for Modular Elliptic Curves Full Canadian Binding by : J. E. Cremona
Download or read book Algorithms for Modular Elliptic Curves Full Canadian Binding written by J. E. Cremona. This book was released on 1997-05-15. Available in PDF, EPUB and Kindle. Book excerpt: This book presents an extensive set of tables giving information about elliptic curves.
Author : J. E. Cremona
Release : 1992
Genre : Algorithme
Kind : eBook
Book Rating : 133/5 ( reviews)
Book Synopsis Algorithms for Modular Elliptic Curves by : J. E. Cremona
Download or read book Algorithms for Modular Elliptic Curves written by J. E. Cremona. This book was released on 1992. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a thorough treatment of many algorithms concerning the arithmetic of elliptic curves with remarks on computer implementation. It is in three parts. First, the author describes in detail the construction of modular elliptic curves, giving an explicit algorithm for their computation using modular symbols. Second, a collection of algorithms for the arithmetic of elliptic curves is presented; some of these have not appeared in book form before. They include: finding torsion and nontorsion points, computing heights, finding isogenies and periods, and computing the rank. Finally, an extensive set of tables is provided giving the results of the author's implementations of the algorithms. These tables extend the widely used "Antwerp IV Tables" in two ways, the range of conductors (up to 1000) and the level of detail given for each curve. In particular the quantities relating to the Birch-Swinnerton-Dyer conjecture have been computed in each case and are included.
Author : N. Koblitz
Release : 2012-12-06
Genre : Mathematics
Kind : eBook
Book Rating : 552/5 ( reviews)
Book Synopsis Introduction to Elliptic Curves and Modular Forms by : N. Koblitz
Download or read book Introduction to Elliptic Curves and Modular Forms written by N. Koblitz. This book was released on 2012-12-06. Available in PDF, EPUB and Kindle. Book excerpt: This textbook covers the basic properties of elliptic curves and modular forms, with emphasis on certain connections with number theory. The ancient "congruent number problem" is the central motivating example for most of the book. My purpose is to make the subject accessible to those who find it hard to read more advanced or more algebraically oriented treatments. At the same time I want to introduce topics which are at the forefront of current research. Down-to-earth examples are given in the text and exercises, with the aim of making the material readable and interesting to mathematicians in fields far removed from the subject of the book. With numerous exercises (and answers) included, the textbook is also intended for graduate students who have completed the standard first-year courses in real and complex analysis and algebra. Such students would learn applications of techniques from those courses, thereby solidifying their under standing of some basic tools used throughout mathematics. Graduate stu dents wanting to work in number theory or algebraic geometry would get a motivational, example-oriented introduction. In addition, advanced under graduates could use the book for independent study projects, senior theses, and seminar work.
Author : Alf J. van der Poorten
Release : 2008-04-25
Genre : Computers
Kind : eBook
Book Rating : 557/5 ( reviews)
Book Synopsis Algorithmic Number Theory by : Alf J. van der Poorten
Download or read book Algorithmic Number Theory written by Alf J. van der Poorten. This book was released on 2008-04-25. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 8th International Algorithmic Number Theory Symposium, ANTS 2008, held in Banff, Canada, in May 2008. The 28 revised full papers presented together with 2 invited papers were carefully reviewed and selected for inclusion in the book. The papers are organized in topical sections on elliptic curves cryptology and generalizations, arithmetic of elliptic curves, integer factorization, K3 surfaces, number fields, point counting, arithmetic of function fields, modular forms, cryptography, and number theory.
Author : Henri Darmon
Release :
Genre : Mathematics
Kind : eBook
Book Rating : 459/5 ( reviews)
Book Synopsis Rational Points on Modular Elliptic Curves by : Henri Darmon
Download or read book Rational Points on Modular Elliptic Curves written by Henri Darmon. This book was released on . Available in PDF, EPUB and Kindle. Book excerpt: The book surveys some recent developments in the arithmetic of modular elliptic curves. It places a special emphasis on the construction of rational points on elliptic curves, the Birch and Swinnerton-Dyer conjecture, and the crucial role played by modularity in shedding light on these two closely related issues. The main theme of the book is the theory of complex multiplication, Heegner points, and some conjectural variants. The first three chapters introduce the background and prerequisites: elliptic curves, modular forms and the Shimura-Taniyama-Weil conjecture, complex multiplication and the Heegner point construction. The next three chapters introduce variants of modular parametrizations in which modular curves are replaced by Shimura curves attached to certain indefinite quaternion algebras. The main new contributions are found in Chapters 7-9, which survey the author's attempts to extend the theory of Heegner points and complex multiplication to situations where the base field is not a CM field. Chapter 10 explains the proof of Kolyvagin's theorem, which relates Heegner points to the arithmetic of elliptic curves and leads to the best evidence so far for the Birch and Swinnerton-Dyer conjecture.
