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椭圆曲线PDF|Epub|txt|kindle电子书版本网盘下载

（美）奈普著著
出版社：北京;西安：世界图书出版公司
ISBN：9787510050664
出版时间：2013
标注页数：427页
文件大小：75MB
文件页数：441页
主题词：椭圆曲线－英文

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图书目录

Ⅰ．Overview3

Ⅱ．Curves in Projective Space19

1．Projective Space19

2．Curves and Tangents24

3．Flexes32

4．Application to Cubics40

5．Bezout's Theorem and Resultants44

Ⅲ．Cubic Curves in Weierstrass Form50

1．Examples50

2．Weierstrass Form,Discriminant,j-invariant56

3．Group Law67

4．Computations with the Group Law74

5．Singular Points77

Ⅳ．Mordell's Theorem80

1．Descent80

2．Condition for Divisibility by 285

3．E(Q)/2E(Q),Special Case88

4．E(Q)/2E(Q),General Case92

5．Height and Mordell's Theorem95

6．Geometric Formula for Rank102

7．Upper Bound on the Rank107

8．Construction of Points in E(Q)115

9．Appendix on Algebraic Number Theory122

Ⅴ．Torsion Subgroup of E(Q)130

1．Overview130

2．Reduction Modulo p134

3．p-adic Filtration137

4．Lutz-Nagell Theorem144

5．Construction of Curves with Prescribed Torsion145

6．Torsion Groups for Special Curves148

Ⅵ．Complex Points151

1．Overview151

2．Elliptic Functions152

3．Weierstrass ？ Function153

4．Effect on Addition162

5．Overview of Inversion Problem165

6．Analytic Continuation166

7．Riemann Surface of the Integrand169

8．An Elliptic Integral174

9．Computability of the Correspondence183

Ⅶ．Dirichlet's Theorem189

1．Motivation189

2．Dirichlet Series and Euler Products192

3．Fourier Analysis on Finite Abelian Groups199

4．Proof of Dirichlet's Theorem201

5．Analytic Properties of Dirichlet L Functions207

Ⅷ．Modular Forms for SL(2,Z)221

1．Overview221

2．Definitions and Examples222

3．Geometry of the q Expansion227

4．Dimensions of Spaces of Modular Forms231

5．L Function of a Cusp Form238

6．Petersson Inner Product241

7．Hecke Operators242

8．Interaction with Petersson Inner Product250

Ⅸ．Modular Forms for Hecke Subgroups256

1．Hecke Subgroups256

2．Modular and Cusp Forms261

3．Examples of Modular Forms265

4．L Function of a Cusp Form267

5．Dimensions of Spaces of Cusp Forms271

6．Hecke Operators273

7．Oldforms and Newforms283

Ⅹ．L Function of an Elliptic Curve290

1．Global Minimal Weierstrass Equations290

2．Zeta Functions and L Functions294

3．Hasse's Theorem296

Ⅺ．Eichler-Shimura Theory302

1．Overview302

2．Riemann surface X0(N)311

3．Meromorphic DifFerentials312

4．Properties of Compact Riemann Surfaces316

5．Hecke Operators on Integral Homology320

6．Modular Function j(T)333

7．Varieties and Curves341

8．Canonical Model of X0(N)349

9．Abstract Elliptic Curves and Isogenies359

10．Abelian Varieties and J acobian Variety367

11．Elliptic Curves Constructed from S2(г0(N)374

12．Match of L Functions383

Ⅻ．Taniyama-Weil Conjecture386

1．Relationships among Conjectures386

2．Strong Weil Curves and Twists392

3．Computations of Equations of Weil Curves394

4．Connection with Fermat's Last Theorem397

Notes401

References409

Index of Notation419

Index423