The Arithmetic of Elliptic Curves

Joseph H. Silverman

ISBN 10: 1441918582 / ISBN 13: 9781441918581

Published by Springer US, Springer New York Nov 2010, 2010

About this Item

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 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.Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 536 pp. Englisch.

Seller Inventory # 9781441918581

Bibliographic Details

• Title: The Arithmetic of Elliptic Curves
• Publisher: Springer US, Springer New York Nov 2010
• Publication Date: 2010
• Language: English
• ISBN 10: 1441918582
• ISBN 13: 9781441918581
• Binding: Taschenbuch
• Condition: Neu

About this title

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.

About the Author

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.