椭圆曲线的有理点 [Rational Points on Elliptic Curves] 下载 mobi epub pdf 电子书 2024

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内容简介

　　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.

内页插图

目录

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

椭圆曲线的有理点 [Rational Points on Elliptic Curves] 下载 mobi epub pdf txt 电子书 格式

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发货到货快，包装仔细，内容深入浅出，适用于几何学相关方向的学习。

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很有趣的书，讲解由浅入深，很喜欢！

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本书是非常赞，好不容易有了一个影印版本，盼星星盼月亮终于能买到了。椭圆曲线是经典的研究课题，有理点也是令人喜爱，爱不释手。本来，这个书应该打五星。但是，世界图书出的这个版本已经过时：第二版已经好像在世图出眼前的这个书之前已经出版。换句话，世图的这个影印版已经木有任何意义

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