The Arithmetic of Elliptic Curves
The Arithmetic of Elliptic Curves
Résumé
Treats the arithmetic theory of elliptic curves in its modern formulation through the use of basic algebraic number theory and algebraic geometry. This book outlines necessary algebro-geometric results and offers an exposition of the geometry of elliptic curves, the formal group of an elliptic curve, and elliptic curves over finite fields.
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The Arithmetic of Elliptic Curves by Joseph Silverman
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. 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.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.
| SKU | Non disponible |
| ISBN 13 | 9780387962030 |
| ISBN 10 | 0387962034 |
| Titre | The Arithmetic of Elliptic Curves |
| Auteur | Joseph Silverman |
| Série | Graduate Texts In Mathematics |
| État | Non disponible |
| Type de reliure | Hardback |
| Éditeur | Springer-Verlag New York Inc. |
| Année de publication | 1985-12-01 |
| Nombre de pages | 412 |
| Note de couverture | La photo du livre est présentée à titre d'illustration uniquement. La reliure, la couverture ou l'édition réelle peuvent varier. |
| Note | Non disponible |