椭圆曲线的有理点 [Rational Points on Elliptic Curves] pdf epub mobi txt 电子书 下载 2025

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[美] 西尔弗曼（Silverman J.H.） 著

出版社： 世界图书出版公司

ISBN：9787510086328

版次：1

商品编码：11647744

包装：平装

外文名称：Rational Points on Elliptic Curves

开本：24开

出版时间：2015-01-01

用纸：胶版纸

页数：281

正文语种：英文

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.

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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

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评分☆☆☆☆☆

因为从外地调货，所以时间长了点，不过总体很好，在京东买东西还是很方便。

评分☆☆☆☆☆

因为从外地调货，所以时间长了点，不过总体很好，在京东买东西还是很方便。

评分☆☆☆☆☆

好

评分☆☆☆☆☆

很不错的书，值得专业人士阅读。