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Synopsis
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 theory of elliptic curves in its modern formulation, through the use of basic algebraic number theory and algebraic geometry. The book begins with a brief discussion of the necessary algebro-geometric results, and 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. The last two chapters deal with integral and rational points, including Siegel’s theorem and explicit computations for the curve Y^2 = X^3 + DX.
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À propos de l?auteur
Dr. Joseph Silverman is a professor at Brown University and has been an instructor or professors since 1982. He was the Chair of the Brown Mathematics department from 2001-2004. He has received numerous fellowships, grants and awards, as well as being a frequently invited lecturer. He is currently a member of the Council of the American Mathematical Society. His research areas of interest are number theory, arithmetic geometry, elliptic curves, dynamical systems and cryptography. He has co-authored over 120 publications and has had over 20 doctoral students under his tutelage. He has published 9 highly successful books with Springer, including the recently released, An Introduction to Mathematical Cryptography, for Undergraduate Texts in Mathematics.
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The Arithmetic of Elliptic Curves (Graduate Texts in Mathematics, 106)
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Springer, 2010
ISBN 10 : 1441918582
ISBN 13 : 9781441918581
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Etat : good. Fast Free Shipping â" Good condition book with a firm cover and clean, readable pages. Shows normal use, including some light wear or limited notes highlighting, yet remains a dependable copy overall. Supplemental items like CDs or access codes may not be included. N° de réf. du vendeur GWV.1441918582.G
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Arithmetic of Elliptic Curves
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The Arithmetic of Elliptic Curves
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Springer New York Nov 2010, 2010
ISBN 10 : 1441918582
ISBN 13 : 9781441918581
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Taschenbuch. Etat : Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -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 theory of elliptic curves in its modern formulation, through the use of basic algebraic number theory and algebraic geometry. The book begins with a brief discussion of the necessary algebro-geometric results, and proceeds with an exposition of the geometry of elliptic curves, the formal group of an elliptic curve, and elliptic curves over finite fields, the complex numbers, local fields, and global fields. Included are proofs of the Mordell Weil theorem giving finite generation of the group of rational points and Siegel's theorem on finiteness of integral points.For this second edition of The Arithmetic of Elliptic Curves, there is a new chapter entitled Algorithmic Aspects of Elliptic Curves, with an emphasis on algorithms over finite fields which have cryptographic applications. These include Lenstra's factorization algorithm, Schoof's point counting algorithm, Miller's algorithm to compute the Tate and Weil pairings, and a description of aspects of elliptic curve cryptography. There is also a new section on Szpiro's conjecture and ABC, as well as expanded and updated accounts of recent developments and numerous new exercises.The book contains three appendices: Elliptic Curves in Characteristics 2 and 3, Group Cohomology, and a third appendix giving an overview of more advanced topics. 536 pp. Englisch. N° de réf. du vendeur 9781441918581
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Arithmetic of Elliptic Curves
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The Arithmetic of Elliptic Curves
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