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整权与半整权模形式 英文2025|PDF|Epub|mobi|kindle电子书版本百度云盘下载

整权与半整权模形式 英文
  • Xueli Wang， Dingyi Pei 著
  • 出版社： 北京：科学出版社
  • ISBN：9787030330796
  • 出版时间：2012
  • 标注页数：432页
  • 文件大小：11MB
  • 文件页数：441页
  • 主题词：函数论－研究－英文

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图书目录

Chapter 1 Theta Functions and Their Transformation Formulae1

Chapter 2 Eisenstein Series13

2.1 Eisenstein Series with Half Integral Weight13

2.2 Eisenstein Series with Integral Weight37

Chapter 3 The Modular Group and Its Subgroups45

Chapter 4 Modular Forms with Integral Weight or Half-integral Weight65

4.1 Dimension Formula for Modular Forms with Integral Weight65

4.2 Dimension Formula for Modular Forms with Half-Integral Weight81

References88

Chapter 5 Operators on the Space of Modular Forms89

5.1 Hecke Rings89

5.2 A Representation of the Hecke Ring on the Space of Modular Forms113

5.3 Zeta Functions of Modular Forms,Functional Equation,Weil Theorem120

5.4 Hecke Operators on the Space of Modular Forms with Half-Integral Weight134

References152

Chapter 6 New Forms and Old Forms153

6.1 New Forms with Integral Weight153

6.2 New Forms with Half Integral Weight178

6.3 Dimension Formulae for the Spaces of New Forms200

Chapter 7 Construction of Eisenstein Series205

7.1 Construction of Eisenstein Series with Weight≥5/2205

7.2 Construction of Eisenstein Series with Weight 1/2221

7.3 Construction of Eisenstein Series with Weight 3/2232

7.4 Construction of Cohen-Eisenstein Series246

7.5 Construction of Eisenstein Series with Integral Weight255

References263

Chapter 8 Weil Representation and Shimura Lifting265

8.1 Weil Representation265

8.2 Shimura Lifting for Cusp Forms280

8.3 Shimura Lifting of Eisenstein Spaces299

8.4 A Congruence Relation between Some Modular Forms309

References318

Chapter 9 Trace Formula321

9.1 Eichler-Selberg Trace Formula on SL2(Z)321

9.2 Eichler-Selberg Trace Formula on Fuchsian Groups335

9.3 Trace Formula on the Space Sk+1/2(N,X)348

References362

Chapter 10 Integers Represented by Positive Definite Quadratic Forms363

10.1 Theta Function of a Positive Definite Quadratic Form and Its Values at Cusp Points363

10.2 The Minimal Integer Represented by a Positive Definite Quadratic Form376

10.3 The Eligible Numbers of a Positive Definite Ternary Quadratic Form390

References428

Index431

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