The Arithmetic of Elliptic Curves / Edition 2

The Arithmetic of Elliptic Curves / Edition 2

by Joseph H. Silverman
ISBN-10:
1441918582
ISBN-13:
9781441918581
Pub. Date:
11/19/2010
Publisher:
Springer New York

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Overview

The Arithmetic of Elliptic Curves / Edition 2

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.

Product Details

ISBN-13: 9781441918581
Publisher: Springer New York
Publication date: 11/19/2010
Series: Graduate Texts in Mathematics , #106
Edition description: Softcover reprint of hardcover 2nd ed. 2009
Pages: 513
Sales rank: 992,828
Product dimensions: 6.10(w) x 9.25(h) x 0.36(d)

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 frequentlyinvited 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 published9 highly successful books with Springer,including the recently released, An Introduction to Mathematical Cryptography, for Undergraduate Texts in Mathematics.

Table of Contents

Algebraic Varieties.- Algebraic Curves.- The Geometry of Elliptic Curves.- The Formal Group of an Elliptic Curve.- Elliptic Curves over Finite Fields.- Elliptic Curves over C.- Elliptic Curves over Local Fields.- Elliptic Curves over Global Fields.- Integral Points on Elliptic Curves.- Computing the Mordell#x2013;Weil Group.- Algorithmic Aspects of Elliptic Curves.

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