Elliptic Curves And Arithmetic Invariants

Elliptic Curves And Arithmetic Invariants Book in PDF, ePub and Kindle version is available to download in english. Read online anytime anywhere directly from your device. Click on the download button below to get a free pdf file of Elliptic Curves And Arithmetic Invariants book. This book definitely worth reading, it is an incredibly well-written.

Elliptic Curves and Arithmetic Invariants

Haruzo Hida
Elliptic Curves and Arithmetic Invariants Book PDF

Author : Haruzo Hida
Publisher : Springer Science & Business Media
Page : 464 pages
File Size : 54,5 Mb
Release : 2013-06-13
Category : Mathematics
ISBN : 9781461466574

Get Book

Elliptic Curves and Arithmetic Invariants by Haruzo Hida Pdf

This book contains a detailed account of the result of the author's recent Annals paper and JAMS paper on arithmetic invariant, including μ-invariant, L-invariant, and similar topics. This book can be regarded as an introductory text to the author's previous book p-Adic Automorphic Forms on Shimura Varieties. Written as a down-to-earth introduction to Shimura varieties, this text includes many examples and applications of the theory that provide motivation for the reader. Since it is limited to modular curves and the corresponding Shimura varieties, this book is not only a great resource for experts in the field, but it is also accessible to advanced graduate students studying number theory. Key topics include non-triviality of arithmetic invariants and special values of L-functions; elliptic curves over complex and p-adic fields; Hecke algebras; scheme theory; elliptic and modular curves over rings; and Shimura curves.

The Arithmetic of Elliptic Curves

Joseph H. Silverman
The Arithmetic of Elliptic Curves Book PDF

Author : Joseph H. Silverman
Publisher : Springer
Page : 514 pages
File Size : 47,7 Mb
Release : 2009-05-29
Category : Mathematics
ISBN : 0387094938

Get Book

The Arithmetic of Elliptic Curves by Joseph H. Silverman Pdf

The theory of elliptic curves is distinguished by its long history and by the diversity of the methods that have been used in its study. This book treats the arithmetic approach in its modern formulation, through the use of basic algebraic number theory and algebraic geometry. Following a brief discussion of the necessary algebro-geometric results, the book proceeds with an exposition of the geometry and the formal group of elliptic curves, elliptic curves over finite fields, the complex numbers, local fields, and global fields. Final chapters deal with integral and rational points, including Siegels theorem and explicit computations for the curve Y = X + DX, while three appendices conclude the whole: Elliptic Curves in Characteristics 2 and 3, Group Cohomology, and an overview of more advanced topics.

Elliptic Curves

Henry McKean,Victor Moll
Elliptic Curves Book PDF

Author : Henry McKean,Victor Moll
Publisher : Cambridge University Press
Page : 300 pages
File Size : 53,9 Mb
Release : 1999-08-13
Category : Mathematics
ISBN : 0521658179

Get Book

Elliptic Curves by Henry McKean,Victor Moll Pdf

An introductory 1997 account in the style of the original discoverers, treating the fundamental themes even-handedly.

Elliptic Curves

Dale Husemoller
Elliptic Curves Book PDF

Author : Dale Husemoller
Publisher : Springer Science & Business Media
Page : 363 pages
File Size : 40,9 Mb
Release : 2013-06-29
Category : Mathematics
ISBN : 9781475751192

Get Book

Elliptic Curves by Dale Husemoller Pdf

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.

Advanced Topics in the Arithmetic of Elliptic Curves

Joseph H. Silverman
Advanced Topics in the Arithmetic of Elliptic Curves Book PDF

Author : Joseph H. Silverman
Publisher : Springer Science & Business Media
Page : 482 pages
File Size : 55,7 Mb
Release : 2013-12-01
Category : Mathematics
ISBN : 9781461208518

Get Book

Advanced Topics in the Arithmetic of Elliptic Curves by Joseph H. Silverman Pdf

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.

Elliptic Curves

Lawrence C. Washington
Elliptic Curves Book PDF

Author : Lawrence C. Washington
Publisher : CRC Press
Page : 533 pages
File Size : 41,6 Mb
Release : 2008-04-03
Category : Computers
ISBN : 9781420071474

Get Book

Elliptic Curves by Lawrence C. Washington Pdf

Like its bestselling predecessor, Elliptic Curves: Number Theory and Cryptography, Second Edition develops the theory of elliptic curves to provide a basis for both number theoretic and cryptographic applications. With additional exercises, this edition offers more comprehensive coverage of the fundamental theory, techniques, and application

One Semester of Elliptic Curves

Torsten Ekedahl
One Semester of Elliptic Curves Book PDF

Author : Torsten Ekedahl
Publisher : European Mathematical Society
Page : 148 pages
File Size : 41,6 Mb
Release : 2006
Category : Mathematics
ISBN : 3037190159

Get Book

One Semester of Elliptic Curves by Torsten Ekedahl Pdf

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.

Elliptic Curves

Lawrence C. Washington
Elliptic Curves Book PDF

Author : Lawrence C. Washington
Publisher : CRC Press
Page : 446 pages
File Size : 43,7 Mb
Release : 2003-05-28
Category : Computers
ISBN : 0203484029

Get Book

Elliptic Curves by Lawrence C. Washington Pdf

Elliptic curves have played an increasingly important role in number theory and related fields over the last several decades, most notably in areas such as cryptography, factorization, and the proof of Fermat's Last Theorem. However, most books on the subject assume a rather high level of mathematical sophistication, and few are truly accessible to

Elliptic Curves

Susanne Schmitt,Horst G. Zimmer
Elliptic Curves Book PDF

Author : Susanne Schmitt,Horst G. Zimmer
Publisher : Walter de Gruyter
Page : 378 pages
File Size : 48,8 Mb
Release : 2008-08-22
Category : Mathematics
ISBN : 9783110198010

Get Book

Elliptic Curves by Susanne Schmitt,Horst G. Zimmer Pdf

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.

Arithmetic Theory of Elliptic Curves

J. Coates,R. Greenberg,K.A. Ribet,K. Rubin
Arithmetic Theory of Elliptic Curves Book PDF

Author : J. Coates,R. Greenberg,K.A. Ribet,K. Rubin
Publisher : Springer
Page : 269 pages
File Size : 53,6 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540481607

Get Book

Arithmetic Theory of Elliptic Curves by J. Coates,R. Greenberg,K.A. Ribet,K. Rubin Pdf

This volume contains the expanded versions of the lectures given by the authors at the C.I.M.E. instructional conference held in Cetraro, Italy, from July 12 to 19, 1997. The papers collected here are broad surveys of the current research in the arithmetic of elliptic curves, and also contain several new results which cannot be found elsewhere in the literature. Owing to clarity and elegance of exposition, and to the background material explicitly included in the text or quoted in the references, the volume is well suited to research students as well as to senior mathematicians.

Algorithms for Modular Elliptic Curves Full Canadian Binding

J. E. Cremona
Algorithms for Modular Elliptic Curves Full Canadian Binding Book PDF

Author : J. E. Cremona
Publisher : CUP Archive
Page : 388 pages
File Size : 48,5 Mb
Release : 1997-05-15
Category : Mathematics
ISBN : 0521598206

Get Book

Algorithms for Modular Elliptic Curves Full Canadian Binding by J. E. Cremona Pdf

This book presents an extensive set of tables giving information about elliptic curves.

Arithmetic Moduli of Elliptic Curves. (AM-108), Volume 108

Nicholas M. Katz,Barry Mazur
Arithmetic Moduli of Elliptic Curves AM 108 Volume 108 Book PDF

Author : Nicholas M. Katz,Barry Mazur
Publisher : Princeton University Press
Page : 528 pages
File Size : 54,8 Mb
Release : 2016-03-02
Category : Mathematics
ISBN : 9781400881710

Get Book

Arithmetic Moduli of Elliptic Curves. (AM-108), Volume 108 by Nicholas M. Katz,Barry Mazur Pdf

This work is a comprehensive treatment of recent developments in the study of elliptic curves and their moduli spaces. The arithmetic study of the moduli spaces began with Jacobi's "Fundamenta Nova" in 1829, and the modern theory was erected by Eichler-Shimura, Igusa, and Deligne-Rapoport. In the past decade mathematicians have made further substantial progress in the field. This book gives a complete account of that progress, including not only the work of the authors, but also that of Deligne and Drinfeld.

The Arithmetic of Elliptic Curves

Joseph H. Silverman
The Arithmetic of Elliptic Curves Book PDF

Author : Joseph H. Silverman
Publisher : Springer Science & Business Media
Page : 414 pages
File Size : 48,8 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9781475719208

Get Book

The Arithmetic of Elliptic Curves by Joseph H. Silverman Pdf

The theory of elliptic curves is distinguished by its long history and by the diversity of the methods that have been used in its study. This book treats the arithmetic approach in its modern formulation, through the use of basic algebraic number theory and algebraic geometry. Following a brief discussion of the necessary algebro-geometric results, the book proceeds with an exposition of the geometry and the formal group of elliptic curves, elliptic curves over finite fields, the complex numbers, local fields, and global fields. Final chapters deal with integral and rational points, including Siegels theorem and explicit computations for the curve Y = X + DX, while three appendices conclude the whole: Elliptic Curves in Characteristics 2 and 3, Group Cohomology, and an overview of more advanced topics.

Elliptic Curves

Anthony W. Knapp
Elliptic Curves Book PDF

Author : Anthony W. Knapp
Publisher : Princeton University Press
Page : 450 pages
File Size : 48,9 Mb
Release : 1992
Category : Mathematics
ISBN : 0691085595

Get Book

Elliptic Curves by Anthony W. Knapp Pdf

An elliptic curve is a particular kind of cubic equation in two variables whose projective solutions form a group. Modular forms are analytic functions in the upper half plane with certain transformation laws and growth properties. The two subjects--elliptic curves and modular forms--come together in Eichler-Shimura theory, which constructs elliptic curves out of modular forms of a special kind. The converse, that all rational elliptic curves arise this way, is called the Taniyama-Weil Conjecture and is known to imply Fermat's Last Theorem. Elliptic curves and the modeular forms in the Eichler- Shimura theory both have associated L functions, and it is a consequence of the theory that the two kinds of L functions match. The theory covered by Anthony Knapp in this book is, therefore, a window into a broad expanse of mathematics--including class field theory, arithmetic algebraic geometry, and group representations--in which the concidence of L functions relates analysis and algebra in the most fundamental ways. Developing, with many examples, the elementary theory of elliptic curves, the book goes on to the subject of modular forms and the first connections with elliptic curves. The last two chapters concern Eichler-Shimura theory, which establishes a much deeper relationship between the two subjects. No other book in print treats the basic theory of elliptic curves with only undergraduate mathematics, and no other explains Eichler-Shimura theory in such an accessible manner.

Rational Points on Modular Elliptic Curves

Henri Darmon
Rational Points on Modular Elliptic Curves Book PDF

Author : Henri Darmon
Publisher : American Mathematical Soc.
Page : 148 pages
File Size : 49,8 Mb
Release : 2024-06-30
Category : Mathematics
ISBN : 0821889451

Get Book

Rational Points on Modular Elliptic Curves by Henri Darmon Pdf

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.