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椭圆曲线算术 第2版 英文 🔍
(美)希尔弗曼著, Joseph H. Silüerman著, 希尔弗曼, Joseph H Silverman 北京/西安:世界图书出版公司, 2011, 2011
英语 [en] · 中文 [zh] · PDF · 16.1MB · 2011 · 📗 未知类型的图书 · 🚀/duxiu/zlibzh · Save
描述
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.
备用文件名
zlibzh/no-category/（美）希尔弗曼著, Joseph H. Silüerman著, 希尔弗曼, Joseph H Silverman/椭圆曲线算术：第2版：英文_40896768.pdf
备选标题
The Arithmetic of Elliptic Curves (Graduate Texts in Mathematics Book 106)
备选标题
The arithmetic of elliptic curves / monograph
备选作者
Silverman, Joseph H.
备用出版商
Springer International Publishing
备用出版商
World Publishing Corporation
备用出版商
Springer London, Limited
备用出版商
World Publishing Company
备用出版商
Springer-Verlag
备用出版商
世界图书出版公司北京公司
备用出版商
Copernicus
备用出版商
Telos
备用版本
Graduate Texts in Mathematics, 106, Second Edition, Cham, 2009
备用版本
Graduate texts in mathematics, 106, 2nd ed, Dordrecht, ©2009
备用版本
Graduate texts in mathematics, 106, 2nd ed, New York, ©2009
备用版本
Graduate texts in mathematics, Beijing, 2011
备用版本
United States, United States of America
备用版本
China, People's Republic, China
备用版本
Ying yin ban, Beijing, 2011
元数据中的注释
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备用描述
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
备用描述
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.
备用描述
Treats the arithmetic theory of elliptic curves in its modern formulation, through the use of basic algebraic number theory and algebraic geometry. This book discusses the necessary algebro-geometric results, and offers an exposition of the geometry of elliptic curves, and the formal group of an elliptic curve
开源日期
2024-06-13
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