The Arithmetic Of Elliptic Curves

Author : Joseph H. Silverman
Publisher : Springer Science & Business Media
Page : 414 pages
File Size : 47,5 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9781475719208

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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.

Author : Joseph H. Silverman
Publisher : Springer Science & Business Media
Page : 482 pages
File Size : 51,9 Mb
Release : 2013-12-01
Category : Mathematics
ISBN : 9781461208518

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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.

Author : B.H. Gross
Publisher : Springer
Page : 100 pages
File Size : 51,6 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540385752

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Arithmetic on Elliptic Curves with Complex Multiplication by B.H. Gross Pdf

Author : Joseph H. Silverman,John Tate
Publisher : Springer Science & Business Media
Page : 292 pages
File Size : 53,6 Mb
Release : 2013-04-17
Category : Mathematics
ISBN : 9781475742527

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Rational Points on Elliptic Curves by Joseph H. Silverman,John Tate Pdf

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.

Author : J. Coates,R. Greenberg,K.A. Ribet,K. Rubin
Publisher : Springer
Page : 269 pages
File Size : 49,6 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540481607

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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.

Author : Haruzo Hida
Publisher : Springer Science & Business Media
Page : 464 pages
File Size : 49,9 Mb
Release : 2013-06-13
Category : Mathematics
ISBN : 9781461466574

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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.

Author : Henry McKean,Victor Moll
Publisher : Cambridge University Press
Page : 300 pages
File Size : 46,6 Mb
Release : 1999-08-13
Category : Mathematics
ISBN : 0521658179

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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.

Author : Dale Husemoller
Publisher : Springer Science & Business Media
Page : 363 pages
File Size : 53,7 Mb
Release : 2013-06-29
Category : Mathematics
ISBN : 9781475751192

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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.

Author : John William Scott Cassels
Publisher : Cambridge University Press
Page : 148 pages
File Size : 43,7 Mb
Release : 1991-11-21
Category : Mathematics
ISBN : 0521425301

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LMSST: 24 Lectures on Elliptic Curves by John William Scott Cassels Pdf

A self-contained introductory text for beginning graduate students that is contemporary in approach without ignoring historical matters.

Author : Neal I. Koblitz
Publisher : Springer Science & Business Media
Page : 262 pages
File Size : 41,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461209096

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Introduction to Elliptic Curves and Modular Forms by Neal I. Koblitz Pdf

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.

Author : Alvaro Lozano-Robledo
Publisher : American Mathematical Soc.
Page : 195 pages
File Size : 54,7 Mb
Release : 2011
Category : Mathematics
ISBN : 9780821852422

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Elliptic Curves, Modular Forms, and Their L-functions by Alvaro Lozano-Robledo Pdf

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. The original simply stated problem can be obscured in the depth of the theory developed to understand it. This book is an introduction to some of these problems, and an overview of the theories used nowadays to attack them, presented so that the number theory is always at the forefront of the discussion. Lozano-Robledo gives an introductory survey of elliptic curves, modular forms, and $L$-functions. His main goal is to provide the reader with the big picture of the surprising connections among these three families of mathematical objects and their meaning for number theory. As a case in point, Lozano-Robledo explains the modularity theorem and its famous consequence, Fermat's Last Theorem. He also discusses the Birch and Swinnerton-Dyer Conjecture and other modern conjectures. The book begins with some motivating problems and includes numerous concrete examples throughout the text, often involving actual numbers, such as 3, 4, 5, $\frac{3344161}{747348}$, and $\frac{2244035177043369699245575130906674863160948472041} {8912332268928859588025535178967163570016480830}$. The theories of elliptic curves, modular forms, and $L$-functions are too vast to be covered in a single volume, and their proofs are outside the scope of the undergraduate curriculum. However, the primary objects of study, the statements of the main theorems, and their corollaries are within the grasp of advanced undergraduates. This book concentrates on motivating the definitions, explaining the statements of the theorems and conjectures, making connections, and providing lots of examples, rather than dwelling on the hard proofs. The book succeeds if, after reading the text, students feel compelled to study elliptic curves and modular forms in all their glory.

Author : Jean-Pierre Serre
Publisher : CRC Press
Page : 203 pages
File Size : 45,7 Mb
Release : 1997-11-15
Category : Mathematics
ISBN : 9781439863862

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Abelian l-Adic Representations and Elliptic Curves by Jean-Pierre Serre Pdf

This classic book contains an introduction to systems of l-adic representations, a topic of great importance in number theory and algebraic geometry, as reflected by the spectacular recent developments on the Taniyama-Weil conjecture and Fermat's Last Theorem. The initial chapters are devoted to the Abelian case (complex multiplication), where one

Author : Ian F. Blake,G. Seroussi,N. Smart
Publisher : Cambridge University Press
Page : 228 pages
File Size : 46,9 Mb
Release : 1999-07-08
Category : Computers
ISBN : 0521653746

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Elliptic Curves in Cryptography by Ian F. Blake,G. Seroussi,N. Smart Pdf

This book summarizes knowledge built up within Hewlett-Packard over a number of years, and explains the mathematics behind practical implementations of elliptic curve systems. Due to the advanced nature of the mathematics there is a high barrier to entry for individuals and companies to this technology. Hence this book will be invaluable not only to mathematicians wanting to see how pure mathematics can be applied but also to engineers and computer scientists wishing (or needing) to actually implement such systems.

Author : Lawrence C. Washington
Publisher : CRC Press
Page : 533 pages
File Size : 52,7 Mb
Release : 2008-04-03
Category : Computers
ISBN : 9781420071474

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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

Author : Joseph H. Silverman
Publisher : Springer Science & Business Media
Page : 513 pages
File Size : 40,5 Mb
Release : 2009-04-20
Category : Mathematics
ISBN : 9780387094946

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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.