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Heegner Modules And Elliptic Curves
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Book Synopsis Heegner Modules and Elliptic Curves by : Martin L. Brown
Download or read book Heegner Modules and Elliptic Curves written by Martin L. Brown and published by Springer. This book was released on 2004-08-30 with total page 523 pages. Available in PDF, EPUB and Kindle. Book excerpt: Heegner points on both modular curves and elliptic curves over global fields of any characteristic form the topic of this research monograph. The Heegner module of an elliptic curve is an original concept introduced in this text. The computation of the cohomology of the Heegner module is the main technical result and is applied to prove the Tate conjecture for a class of elliptic surfaces over finite fields, this conjecture is equivalent to the Birch and Swinnerton-Dyer conjecture for the corresponding elliptic curves over global fields.
Book Synopsis Heegner Modules and Elliptic Curves by :
Download or read book Heegner Modules and Elliptic Curves written by and published by Springer Science & Business Media. This book was released on 2004 with total page 532 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Heegner Points and Rankin L-Series by : Henri Darmon
Download or read book Heegner Points and Rankin L-Series written by Henri Darmon and published by Cambridge University Press. This book was released on 2004-06-21 with total page 386 pages. Available in PDF, EPUB and Kindle. Book excerpt: Thirteen articles by leading contributors on the history of the Gross-Zagier formula and its developments.
Book Synopsis Elliptic Curves and Related Topics by : H. Kisilevsky
Download or read book Elliptic Curves and Related Topics written by H. Kisilevsky and published by American Mathematical Soc.. This book was released on 1994-01-01 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book represents the proceedings of a workshop on elliptic curves held in St. Adele, Quebec, in February 1992. Containing both expository and research articles on the theory of elliptic curves, this collection covers a range of topics, from Langlands's theory to the algebraic geometry of elliptic curves, from Iwasawa theory to computational aspects of elliptic curves. This book is especially significant in that it covers topics comprising the main ingredients in Andrew Wiles's recent result on Fermat's Last Theorem.
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 and published by American Mathematical Soc.. This book was released on with total page 148 pages. 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.
Book Synopsis Introduction to Elliptic Curves and Modular Forms by : Neal I. Koblitz
Download or read book Introduction to Elliptic Curves and Modular Forms written by Neal I. Koblitz and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 262 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Elliptic Curves by : Susanne Schmitt
Download or read book Elliptic Curves written by Susanne Schmitt and published by Walter de Gruyter. This book was released on 2008-08-22 with total page 378 pages. Available in PDF, EPUB and Kindle. Book excerpt: The basics of the theory of elliptic curves should be known to everybody, be he (or she) a mathematician or a computer scientist. Especially everybody concerned with cryptography should know the elements of this theory. The purpose of the present textbook is to give an elementary introduction to elliptic curves. Since this branch of number theory is particularly accessible to computer-assisted calculations, the authors make use of it by approaching the theory under a computational point of view. Specifically, the computer-algebra package SIMATH can be applied on several occasions. However, the book can be read also by those not interested in any computations. Of course, the theory of elliptic curves is very comprehensive and becomes correspondingly sophisticated. That is why the authors made a choice of the topics treated. Topics covered include the determination of torsion groups, computations regarding the Mordell-Weil group, height calculations, S-integral points. The contents is kept as elementary as possible. In this way it becomes obvious in which respect the book differs from the numerous textbooks on elliptic curves nowadays available.
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 and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 258 pages. 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.
Book Synopsis One Semester of Elliptic Curves by : Torsten Ekedahl
Download or read book One Semester of Elliptic Curves written by Torsten Ekedahl and published by European Mathematical Society. This book was released on 2006 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt: These lecture notes grew out of a one semester introductory course on elliptic curves given to an audience of computer science and mathematics students, and assume only minimal background knowledge. After having covered basic analytic and algebraic aspects, putting special emphasis on explaining the interplay between algebraic and analytic formulas, they go on to some more specialized topics. These include the $j$-function from an algebraic and analytic perspective, a discussion of elliptic curves over finite fields, derivation of recursion formulas for the division polynomials, the algebraic structure of the torsion points of an elliptic curve, complex multiplication, and modular forms. In an effort to motivate basic problems the book starts very slowly but considers some aspects such as modular forms of higher level which are not usually treated. It presents more than 100 exercises and a Mathematica TM notebook that treats a number of calculations involving elliptic curves. The book is aimed at students of mathematics with a general interest in elliptic curves but also at students of computer science interested in their cryptographic aspects.
Book Synopsis Elliptic Curves by : Dale Husemoller
Download or read book Elliptic Curves written by Dale Husemoller and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 363 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book divides naturally into several parts according to the level of the material, the background required of the reader, and the style of presentation with respect to details of proofs. For example, the first part, to Chapter 6, is undergraduate in level, the second part requires a background in Galois theory and the third some complex analysis, while the last parts, from Chapter 12 on, are mostly at graduate level. A general outline ofmuch ofthe material can be found in Tate's colloquium lectures reproduced as an article in Inven tiones [1974]. The first part grew out of Tate's 1961 Haverford Philips Lectures as an attempt to write something for publication c10sely related to the original Tate notes which were more or less taken from the tape recording of the lectures themselves. This inc1udes parts of the Introduction and the first six chapters The aim ofthis part is to prove, by elementary methods, the Mordell theorem on the finite generation of the rational points on elliptic curves defined over the rational numbers. In 1970 Tate teturned to Haverford to give again, in revised form, the originallectures of 1961 and to extend the material so that it would be suitable for publication. This led to a broader plan forthe book.
Book Synopsis Advanced Topics in the Arithmetic of Elliptic Curves by : Joseph H. Silverman
Download or read book Advanced Topics in the Arithmetic of Elliptic Curves written by Joseph H. Silverman and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 482 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the introduction to the first volume of The Arithmetic of Elliptic Curves (Springer-Verlag, 1986), I observed that "the theory of elliptic curves is rich, varied, and amazingly vast," and as a consequence, "many important topics had to be omitted." I included a brief introduction to ten additional topics as an appendix to the first volume, with the tacit understanding that eventually there might be a second volume containing the details. You are now holding that second volume. it turned out that even those ten topics would not fit Unfortunately, into a single book, so I was forced to make some choices. The following material is covered in this book: I. Elliptic and modular functions for the full modular group. II. Elliptic curves with complex multiplication. III. Elliptic surfaces and specialization theorems. IV. Neron models, Kodaira-Neron classification of special fibers, Tate's algorithm, and Ogg's conductor-discriminant formula. V. Tate's theory of q-curves over p-adic fields. VI. Neron's theory of canonical local height functions.
Book Synopsis Arithmetic of L-functions by : Cristian Popescu
Download or read book Arithmetic of L-functions written by Cristian Popescu and published by American Mathematical Soc.. This book was released on with total page 517 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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 and published by CUP Archive. This book was released on 1997-05-15 with total page 388 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents an extensive set of tables giving information about elliptic curves.
Book Synopsis Elliptic Curves, Modular Forms, and Their L-functions by : Alvaro Lozano-Robledo
Download or read book Elliptic Curves, Modular Forms, and Their L-functions written by Alvaro Lozano-Robledo and published by American Mathematical Soc.. This book was released on with total page 214 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many problems in number theory have simple statements, but their solutions require a deep understanding of algebra, algebraic geometry, complex analysis, group representations, or a combination of all four. This book is an introduction to some of these problems.
Book Synopsis 2-Selmer Groups and Heegner Points on Elliptic Curves by : Chao Li
Download or read book 2-Selmer Groups and Heegner Points on Elliptic Curves written by Chao Li and published by . This book was released on 2015 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This thesis studies several aspects of the arithmetic of elliptic curves. In particular, we explore the prediction of the Birch and Swinnerton-Dyer conjecture when the 2-Selmer group has rank one.
Book Synopsis Drinfeld Modules, Modular Schemes And Applications by : M Van Der Put
Download or read book Drinfeld Modules, Modular Schemes And Applications written by M Van Der Put and published by World Scientific. This book was released on 1997-08-27 with total page 378 pages. Available in PDF, EPUB and Kindle. Book excerpt: In his 1974 seminal paper 'Elliptic modules', V G Drinfeld introduced objects into the arithmetic geometry of global function fields which are nowadays known as 'Drinfeld Modules'. They have many beautiful analogies with elliptic curves and abelian varieties. They study of their moduli spaces leads amongst others to explicit class field theory, Jacquet-Langlands theory, and a proof of the Shimura-Taniyama-Weil conjecture for global function fields.This book constitutes a carefully written instructional course of 12 lectures on these subjects, including many recent novel insights and examples. The instructional part is complemented by research papers centering around class field theory, modular forms and Heegner points in the theory of global function fields.The book will be indispensable for everyone who wants a clear view of Drinfeld's original work, and wants to be informed about the present state of research in the theory of arithmetic geometry over function fields.
Book Synopsis Elliptic Functions and Elliptic Curves by : Patrick Du Val
Download or read book Elliptic Functions and Elliptic Curves written by Patrick Du Val and published by Cambridge University Press. This book was released on 1973-08-02 with total page 257 pages. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensive treatment of elliptic functions is linked by these notes to a study of their application to elliptic curves. This approach provides geometers with the opportunity to acquaint themselves with aspects of their subject virtually ignored by other texts. The exposition is clear and logically carries themes from earlier through to later topics. This enthusiastic work of scholarship is made complete with the inclusion of some interesting historical details and a very comprehensive bibliography.
