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割圆域导论 英文2025|PDF|Epub|mobi|kindle电子书版本百度云盘下载

割圆域导论 英文
  • (美)华盛顿(LAWRENCEC.WASHINGTON)著 著
  • 出版社: 北京:世界图书北京出版公司
  • ISBN:9787510077852
  • 出版时间:2014
  • 标注页数:487页
  • 文件大小:52MB
  • 文件页数:507页
  • 主题词:数论-教材-英文

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图书目录

CHAPTER 1 Fermat's Last Theorem1

CHAPTER 2 Basic Results9

CHAPTER 3 Dirichlet Characters20

CHAPTER 4 Dirichlet L-series and Class Number Formulas30

CHAPTER 5 p-adic L-functions and Bernoulli Numbers47

5.1.p-adic functions47

5.2.p-adic L-functions55

5.3.Congruences59

5.4.The value at s=163

5.5.The p-adic regulator70

5.6.Applications of the class number formula77

CHAPTER 6 Stickelberger's Theorem87

6.1.Gauss sums87

6.2.Stickelberger's theorem93

6.3.Herbrand's theorem100

6.4.The index of the Stickeiberger ideal102

6.5.Fermat's Last Theorem107

CHAPTER 7 Iwasawa's Construction of p-adic L-functions113

7.1.Group tings and power series113

7.2.p-adic L-functions117

7.3.Applications125

7.4.Function fields128

7.5.μ=0130

CHAPTER 8 Cyclotomic Units143

8.1.Cyclotomic units143

8.2.Proof of the p-adic class number formula151

8.3.Units of Q(ξp)and Vandiver's conjecture153

8.4.p-adic expansions159

CHAPTER 9 The Second Case of Fermat's Last Theorem167

9.1.The basic argument167

9.2.The theorems173

CHAPrER 10 Galois Groups Acting on Ideal Class Groups185

10.1.Some theorems on class groups185

10.2.Reflection theorems188

10.3.Consequences of Vandiver's conjecture196

CHAPTER 11 Cyclotomic Fields of Class Numher One205

11.1.The estimate for even characters206

11.2.The estimate for all characters211

11.3.The estimate for h- m217

11.4.Odlyzko's bounds on discriminants221

11.5.Calculation of h+ m228

CHAPTER 12 Measures and Distributions232

12.1.Distributions232

12.2.Measures237

12.3.Universal distributions252

CHAPrER 13 Iwasawa's Theory of Zp-extensions264

13.1.Basic facts265

13.2.The structure of ?-modules269

13.3.Iwasawa's theorem277

13.4.Consequences285

13.5.The maximal abelian p-extension unramified outside p292

13.6.The main conjecture297

13.7.Logarithmic derivatives301

13.8.Local units modulo cyclotomic units312

CHAPTER 14 The Kronecker-Weber Theorem321

CHAPTER 15 The Main Conjecture and Annihilation of Class Groups332

15.1.Stickelberger's theorem332

15.2.Thaine's theorem334

15.3.The converse of Herbrand's theorem341

15.4.The Main Coniecture348

15.5.Adjoints351

15.6.Technical results from Iwasawa theory360

15.7.Proof of the Main Conjecture369

CHAPrER 16 Miscellany373

16.1.Primality testing using Jaeobi sums373

16.2.Sinnott's proof that μ=0380

16.3.The non-p-part of the class number in a Zp-extension385

Appendix391

1.Inverse limits391

2.Infinite Galois theory and ramification theory392

3.Class field theory396

Tables407

1.Bernoulli numbers407

2.Irregular primes410

3.Relative class numbers412

4.Real class numbers420

Bibliography424

List of Symbols483

Index485

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