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Author : J. E. Cremona
Publisher : CUP Archive
Page : 388 pages
File Size : 49,5 Mb
Release : 1997-05-15
Category : Mathematics
ISBN : 0521598206
This book presents an extensive set of tables giving information about elliptic curves.
Author : J. E. Cremona
Publisher : Unknown
Page : 343 pages
File Size : 45,6 Mb
Release : 1992
Category : Algorithme
ISBN : 0521418135
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 : Alf J. van der Poorten,Andreas Stein
Publisher : Springer
Page : 463 pages
File Size : 47,8 Mb
Release : 2008-05-07
Category : Computers
ISBN : 9783540794561
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 : Alf J. van der Poorten,Andreas Stein
Publisher : Springer Science & Business Media
Page : 463 pages
File Size : 53,6 Mb
Release : 2008-04-25
Category : Computers
ISBN : 9783540794554
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
Publisher : Unknown
Page : 129 pages
File Size : 50,9 Mb
Release : 2003
Category : Curves, Elliptic
ISBN : 1470424622
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.
Author : Henri Darmon
Publisher : American Mathematical Soc.
Page : 148 pages
File Size : 49,5 Mb
Release : 2024-07-01
Category : Mathematics
ISBN : 0821889451
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.
Author : William A. Stein
Publisher : American Mathematical Soc.
Page : 290 pages
File Size : 54,8 Mb
Release : 2007-02-13
Category : Mathematics
ISBN : 9780821839607
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.
Author : Anonim
Publisher : Unknown
Page : 1524 pages
File Size : 48,7 Mb
Release : 2004
Category : Mathematics
ISBN : UVA:X006180727
Author : Prosenjit Bose,Pat Morin
Publisher : Springer Science & Business Media
Page : 668 pages
File Size : 54,6 Mb
Release : 2002-11-08
Category : Mathematics
ISBN : 9783540001423
This book constitutes the refereed proceedings of the 13th Annual International Symposium on Algorithms and Computation, ISAAC 2002, held in Vancouver, BC, Canada in November 2002. The 54 revised full papers presented together with 3 invited contributions were carefully reviewed and selected from close to 160 submissions. The papers cover all relevant topics in algorithmics and computation, in particular computational geometry, algorithms and data structures, approximation algorithms, randomized algorithms, graph drawing and graph algorithms, combinatorial optimization, computational biology, computational finance, cryptography, and parallel and distributedd algorithms.
Author : Prosenjit K. Bose,Pat Morin
Publisher : Springer
Page : 662 pages
File Size : 42,8 Mb
Release : 2003-08-02
Category : Mathematics
ISBN : 9783540361367
This book constitutes the refereed proceedings of the 13th Annual International Symposium on Algorithms and Computation, ISAAC 2002, held in Vancouver, BC, Canada in November 2002. The 54 revised full papers presented together with 3 invited contributions were carefully reviewed and selected from close to 160 submissions. The papers cover all relevant topics in algorithmics and computation, in particular computational geometry, algorithms and data structures, approximation algorithms, randomized algorithms, graph drawing and graph algorithms, combinatorial optimization, computational biology, computational finance, cryptography, and parallel and distributedd algorithms.
Author : Yasuhito Kawano,Michele Mosca
Publisher : Springer Science & Business Media
Page : 122 pages
File Size : 52,8 Mb
Release : 2008-10-23
Category : Computers
ISBN : 9783540893035
This book constitutes the thoroughly refereed post-workshop proceedings of the Third Workshop on Theory of Quantum Computation, Communication, and Cryptography, TQC 2008, held in Tokyo, Japan, in January/February 2008. The 10 revised full papers presented were carefully selected during two rounds of reviewing and improvement. The papers present current original research and focus on theoretical aspects of quantum computation, quantum communication, and quantum cryptography, which are part of a larger interdisciplinary field that casts information science in a quantum mechanical framework.
Author : Henri Darmon,Shou-wu Zhang
Publisher : Cambridge University Press
Page : 386 pages
File Size : 47,6 Mb
Release : 2004-06-21
Category : Mathematics
ISBN : 052183659X
Thirteen articles by leading contributors on the history of the Gross-Zagier formula and its developments.
Author : Neal Koblitz
Publisher : Springer Science & Business Media
Page : 393 pages
File Size : 42,7 Mb
Release : 2009-05-03
Category : Mathematics
ISBN : 9783540740780
Neal Koblitz is a co-inventor of one of the two most popular forms of encryption and digital signature, and his autobiographical memoirs are collected in this volume. Besides his own personal career in mathematics and cryptography, Koblitz details his travels to the Soviet Union, Latin America, Vietnam and elsewhere; political activism; and academic controversies relating to math education, the C. P. Snow "two-culture" problem, and mistreatment of women in academia. These engaging stories fully capture the experiences of a student and later a scientist caught up in the tumultuous events of his generation.
Author : Guillaume Hanrot,Francois Morain,Emmanuel Thomé
Publisher : Springer
Page : 397 pages
File Size : 53,6 Mb
Release : 2010-07-08
Category : Computers
ISBN : 9783642145186
This book constitutes the refereed proceedings of the 9th International Algorithmic Number Theory Symposium, ANTS 2010, held in Nancy, France, in July 2010. The 25 revised full papers presented together with 5 invited papers were carefully reviewed and selected for inclusion in the book. The papers are devoted to algorithmic aspects of number theory, including elementary number theory, algebraic number theory, analytic number theory, geometry of numbers, algebraic geometry, finite fields, and cryptography.
Author : Joseph H. Silverman,John Tate
Publisher : Springer Science & Business Media
Page : 292 pages
File Size : 48,8 Mb
Release : 2013-04-17
Category : Mathematics
ISBN : 9781475742527
The theory of elliptic curves involves a blend of algebra, geometry, analysis, and number theory. This book stresses this interplay as it develops the basic theory, providing an opportunity for readers to appreciate the unity of modern mathematics. The book’s accessibility, the informal writing style, and a wealth of exercises make it an ideal introduction for those interested in learning about Diophantine equations and arithmetic geometry.