图书介绍
椭圆曲线上的有理点 英文版PDF|Epub|txt|kindle电子书版本网盘下载
- （美）西尔弗曼著 著
- 出版社： 北京：世界图书北京出版公司
- ISBN：9787510086328
- 出版时间：2015
- 标注页数：284页
- 文件大小：41MB
- 文件页数：294页
- 主题词：椭圆曲线－英文
PDF下载
下载说明
椭圆曲线上的有理点 英文版PDF格式电子书版下载
下载的文件为RAR压缩包。需要使用解压软件进行解压得到PDF格式图书。建议使用BT下载工具Free Download Manager进行下载,简称FDM(免费,没有广告,支持多平台）。本站资源全部打包为BT种子。所以需要使用专业的BT下载软件进行下载。如BitComet qBittorrent uTorrent等BT下载工具。迅雷目前由于本站不是热门资源。不推荐使用！后期资源热门了。安装了迅雷也可以迅雷进行下载！
（文件页数 要大于 标注页数，上中下等多册电子书除外）
注意：本站所有压缩包均有解压码： 点击下载压缩包解压工具
图书目录
Introduction1
CHAPTER ⅠGeometry and Arithmetic9
1．Rational Points on Conics9
2．The Geometry of Cubic Curves15
3．Weierstrass Normal Form22
4．Explicit Formulas for the Group Law28
Exercises32
CHAPTER Ⅱ Points of Finite Order38
1．Points of Order Two and Three38
2．Real and Complex Points on Cubic Curves41
3．The Discriminant47
4．Points of Finite Order Have Integer Coordinates49
5．The Nagell-Lutz Theorem and Further Developments56
Exercises58
CHAPTER Ⅲ The Group of Rational Points63
1．Heights and Descent63
2．The Height of P+P068
3．The Height of 2P71
4．A Useful Homomorphism76
5．Mordell's Theorem83
6．Examples and Further Developments89
7．Singular Cubic Curves99
Exercises102
CHAPTER Ⅳ Cubic Curves over Finite Fields107
1．Rational Points over Finite Fields107
2．A Theorem of Gauss110
3．Points of Finite Order Revisited121
4．A Factorization Algorithm Using Elliptic Curves125
Exercises138
CHAPTER ⅤInteger Points on Cubic Curves145
1．How Many Integer Points?145
2．Taxicabs and Sums of Two Cubes147
3．Thue's Theorem and Diophantine Approximation152
4．Construction of an Auxiliary Polynomial157
5．The Auxiliary Polynomial Is Small165
6．The Auxiliary Polynomial Does Not Vanish168
7．Proof of the Diophantine Approximation Theorem171
8．Further Developments174
Exercises177
CHAPTER Ⅵ Complex Multiplication180
1．Abelian Extensions of Q180
2．Algebraic Points on Cubic Curves185
3．A Galois Representation193
4．Complex Multiplication199
5．Abelian Extensions of Q(i)205
Exercises213
APPENDIX A Projective Geometry220
1．Homogeneous Coordinates and the Projective Plane220
2．Curves in the Projective Plane225
3．Intersections of Projective Curves233
4．Intersection Multiplicities and a Proof of Bezout's Theorem242
5．Reduction Modulo p251
Exercises254
Bibliography259
List of Notation263
Index267