Arithmetic On Elliptic Curves With Complex Multiplication

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Advanced Topics in the Arithmetic of Elliptic Curves

Author : Joseph H. Silverman
Publisher : Springer Science & Business Media
Page : 482 pages
File Size : 40,5 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.

Arithmetic Theory of Elliptic Curves

Author : J. Coates,R. Greenberg,K.A. Ribet,K. Rubin
Publisher : Springer
Page : 269 pages
File Size : 45,8 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.

Elliptic Curves

Author : Dale Husemoller
Publisher : Springer Science & Business Media
Page : 363 pages
File Size : 48,6 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.

Rational Points on Elliptic Curves

Author : Joseph H. Silverman,John Tate
Publisher : Springer Science & Business Media
Page : 292 pages
File Size : 43,6 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.

Treating Child and Adolescent Aggression Through Bibliotherapy

Author : Zipora Shechtman
Publisher : Springer
Page : 239 pages
File Size : 41,5 Mb
Release : 2008-11-06
Category : Psychology
ISBN : 0387097430

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Treating Child and Adolescent Aggression Through Bibliotherapy by Zipora Shechtman Pdf

Antisocial acts by children and teens are on the rise – from verbal abuse to physical bullying to cyber-threats to weapons in schools. Strictly punitive responses to aggressive behaviour may even escalate a situation, leaving peers, parents, and teachers feeling helpless. This unique volume conceptualizes aggression as a symptom of underlying behavioural and emotional problems and examines the psychology of perpetrators and the power dynamics that foster intentionally hurtful behaviour in young people. It details for readers how bibliotherapy offers relevant, innovative, and flexible treatment – as a standalone intervention or as a preventive method in conjunction with other forms of treatment – and can be implemented with individuals and groups, parents, teachers, and even rivals. This unique, must-have resource is essential reading for school psychologists, school counselors, social workers, and clinical child psychologists and any allied educational and mental health professionals who work with troubled youth.

Elliptic Curves

Author : Susanne Schmitt,Horst G. Zimmer
Publisher : Walter de Gruyter
Page : 378 pages
File Size : 45,9 Mb
Release : 2008-08-22
Category : Mathematics
ISBN : 9783110198010

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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.

The Arithmetic of Elliptic Curves

Author : Joseph H. Silverman
Publisher : Springer Science & Business Media
Page : 414 pages
File Size : 51,6 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.

The Arithmetic of Elliptic Curves

Author : Joseph H. Silverman
Publisher : Springer
Page : 400 pages
File Size : 49,8 Mb
Release : 1986
Category : Mathematics
ISBN : 9780387962030

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The Arithmetic of Elliptic Curves by Joseph H. Silverman Pdf

This book treats the arithmetic theory of elliptic curves in its modern formulation through the use of basic algebraic number theory and algebraic geometry. It outlines necessary algebro-geometric results then proceeds with an exposition of the geometry of elliptic curves, the formal group of an elliptic curve, elliptic curves over finite fields, the complex numbers, local fields, and global fields. It also covers integral and rational points.

Abelian l-Adic Representations and Elliptic Curves

Author : Jean-Pierre Serre
Publisher : CRC Press
Page : 203 pages
File Size : 48,6 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

LMSST: 24 Lectures on Elliptic Curves

Author : John William Scott Cassels
Publisher : Cambridge University Press
Page : 148 pages
File Size : 44,9 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.

Complex Multiplication

Author : Reinhard Schertz
Publisher : Cambridge University Press
Page : 128 pages
File Size : 54,6 Mb
Release : 2010-04-29
Category : Mathematics
ISBN : 9781139486835

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Complex Multiplication by Reinhard Schertz Pdf

This is a self-contained 2010 account of the state of the art in classical complex multiplication that includes recent results on rings of integers and applications to cryptography using elliptic curves. The author is exhaustive in his treatment, giving a thorough development of the theory of elliptic functions, modular functions and quadratic number fields and providing a concise summary of the results from class field theory. The main results are accompanied by numerical examples, equipping any reader with all the tools and formulas they need. Topics covered include: the construction of class fields over quadratic imaginary number fields by singular values of the modular invariant j and Weber's tau-function; explicit construction of rings of integers in ray class fields and Galois module structure; the construction of cryptographically relevant elliptic curves over finite fields; proof of Berwick's congruences using division values of the Weierstrass p-function; relations between elliptic units and class numbers.