Algorithms For Modular Elliptic Curves Full Canadian Binding
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Algorithms For Modular Elliptic Curves Full Canadian Binding
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Author : J. E. Cremona
language : en
Publisher: CUP Archive
Release Date : 1997-05-15
Algorithms For Modular Elliptic Curves Full Canadian Binding written by J. E. Cremona and has been published by CUP Archive this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-05-15 with Mathematics categories.
This book presents an extensive set of tables giving information about elliptic curves.
Algorithms For Modular Elliptic Curves
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Author : J. E. Cremona
language : en
Publisher:
Release Date : 1992
Algorithms For Modular Elliptic Curves written by J. E. Cremona and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992 with Algorithme categories.
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.
Algorithmic Number Theory
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Author : Alf J. van der Poorten
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-04-25
Algorithmic Number Theory written by Alf J. van der Poorten and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-04-25 with Computers categories.
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.
Rational Points On Modular Elliptic Curves
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Author : Henri Darmon
language : en
Publisher:
Release Date : 2003
Rational Points On Modular Elliptic Curves written by Henri Darmon and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Curves, Elliptic categories.
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 t.
Introduction To Elliptic Curves And Modular Forms
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Author : Neal I. Koblitz
language : en
Publisher: Springer
Release Date : 2012-11-21
Introduction To Elliptic Curves And Modular Forms written by Neal I. Koblitz and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-11-21 with Mathematics categories.
The theory of elliptic curves and modular forms provides a fruitful meeting ground for such diverse areas as number theory, complex analysis, algebraic geometry, and representation theory. This book starts out with a problem from elementary number theory and proceeds to lead its reader into the modern theory, covering such topics as the Hasse-Weil L-function and the conjecture of Birch and Swinnerton-Dyer. This new edition details the current state of knowledge of elliptic curves.
Elliptic Curves And Modular Forms In Algebraic Topology
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Author : Peter S. Landweber
language : en
Publisher:
Release Date : 2014-01-15
Elliptic Curves And Modular Forms In Algebraic Topology written by Peter S. Landweber and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-15 with categories.
Elliptic Curves Modular Forms And Fermat S Last Theorem
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Author : John Henry Coates
language : en
Publisher:
Release Date : 1997
Elliptic Curves Modular Forms And Fermat S Last Theorem written by John Henry Coates and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997 with Curves, Elliptic categories.
Rational Points On Modular Elliptic Curves
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Author : Henri Darmon
language : en
Publisher: American Mathematical Soc.
Release Date :
Rational Points On Modular Elliptic Curves written by Henri Darmon and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on with Mathematics categories.
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.
Mathematical Reviews
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Author :
language : en
Publisher:
Release Date : 2004
Mathematical Reviews written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Mathematics categories.
Modular Forms A Computational Approach
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Author : William A. Stein
language : en
Publisher: American Mathematical Soc.
Release Date : 2007-02-13
Modular Forms A Computational Approach written by William A. Stein and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-02-13 with Mathematics categories.
This marvellous and highly original book fills a significant gap in the extensive literature on classical modular forms. This is not just yet another introductory text to this theory, though it could certainly be used as such in conjunction with more traditional treatments. Its novelty lies in its computational emphasis throughout: Stein not only defines what modular forms are, but shows in illuminating detail how one can compute everything about them in practice. This is illustrated throughout the book with examples from his own (entirely free) software package SAGE, which really bring the subject to life while not detracting in any way from its theoretical beauty. The author is the leading expert in computations with modular forms, and what he says on this subject is all tried and tested and based on his extensive experience. As well as being an invaluable companion to those learning the theory in a more traditional way, this book will be a great help to those who wish to use modular forms in applications, such as in the explicit solution of Diophantine equations. There is also a useful Appendix by Gunnells on extensions to more general modular forms, which has enough in it to inspire many PhD theses for years to come. While the book's main readership will be graduate students in number theory, it will also be accessible to advanced undergraduates and useful to both specialists and non-specialists in number theory. --John E. Cremona, University of Nottingham William Stein is an associate professor of mathematics at the University of Washington at Seattle. He earned a PhD in mathematics from UC Berkeley and has held positions at Harvard University and UC San Diego. His current research interests lie in modular forms, elliptic curves, and computational mathematics.