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內容簡介

　　The theory of elliptic curves involves a blend of algebra，geometry， analysis，and number theory.This book stresses this interplay as it develops the basic theory，providing an opportunity for readers to appreciate the unity of modern mathematics.The book s accessibility，the informal writing style，and a wealth of exercises make it an ideal introduction for those interested in learning about Diophantine equations and arithmetic geometry.

內頁插圖

目錄

Preface
Computer Packages
Acknowledgments
Introduction
CHAPTER 1
Geometry and Arithmetic
1.Rational Points on Conics
2.The Geometry of Cubic Curves
3.Weierstrass Normal Form
4.Explicit Formulas for the Group Law
Exercises

CHAPTER 2
Points of Finite Order
1.Points of Order Two and Three
2.Real and Complex Points on Cubic Curves
3.The Discriminant
4.Points of Finite Order Have Integer Coordinates
5.The Nagell—Lutz Theorem and Further Developments
Exercises

CHAPTER 3
The Group of Rational Points
1.Heights and Descent
2.The Height of P + P0
3.The Height of 2P
4.A Useful Homomorphism
5.Mordell's Tneorem
6.Examples and Further Developments
7.Singular Cubic Curves
Exercises

CHAPTER 4
Cubic Curves over Finite Fields
1.Rational Points over Finite Fields
2.A Theorem of Gauss
3.Points of Finite Order Revisited
4.A Factorization Algorithm Using Elliptic Curves
Exercises

CHAPTER 5
Integer Points on Cubic Curves
1.How Many Integer Points？
2.Taxicabs and Sums of Two Cubes
3.Thue's Theorem and Diophantine Approximation
4.Construction of an Auxiliary Polynomial
5.The Auxiliary Polynomialls Small
6.The Auxiliary Polynomial Does Not Vanish
7.Proof of the Diophantine Approximation Theorem
8.Further Developments
Exercises

CHAPTER 6
Complex Multiplication
1.Abelian Extensions of Q
2.Algebraic Points on Cubic Curves
3.A Galois Representation
4.Complex Multiplication
5.Abelian Extensions of Q（i）
Exercises

APPENDIX A
Projective Geometry
1.Homogeneous Coordinates and the Projective Plane
2.Curves in the Projective Plane
3.Intersections of Projective Curves
4.Intersection Multiplicities and a Proof of Bezout's Theorem
5.Reduction Modulo p
Exercises
Bibliography
List of Notation
Index

前言/序言

橢圓麯綫的有理點 [Rational Points on Elliptic Curves] 下載 mobi epub pdf txt 電子書

評分☆☆☆☆☆

好

評分☆☆☆☆☆

很有趣的書，講解由淺入深，很喜歡！

評分☆☆☆☆☆

好

評分☆☆☆☆☆

書的內容很好！！！！

評分☆☆☆☆☆

橢圓麯綫算術理論入門的經典之作，起點比較低。不過就是因為起點過低，所以在缺乏現代工具的條件下有些問題的討論顯得比較復雜。

評分☆☆☆☆☆

課餘讀物，比較直觀，通讀有益

評分☆☆☆☆☆

本書是非常贊，好不容易有瞭一個影印版本，盼星星盼月亮終於能買到瞭。橢圓麯綫是經典的研究課題，有理點也是令人喜愛，愛不釋手。本來，這個書應該打五星。但是，世界圖書齣的這個版本已經過時：第二版已經好像在世圖齣眼前的這個書之前已經齣版。換句話，世圖的這個影印版已經木有任何意義

評分☆☆☆☆☆

看起來還不錯，排版一般吧

評分☆☆☆☆☆

很好很適閤學生老師閱讀

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