割圆域导论 英文PDF电子书下载

CHAPTER 1 Fermat's Last Theorem 1

CHAPTER 2 Basic Results 9

CHAPTER 3 Dirichlet Characters 20

CHAPTER 4 Dirichlet L-series and Class Number Formulas 30

CHAPTER 5 p-adic L-functions and Bernoulli Numbers 47

5.1．p-adic functions 47

5.2．p-adic L-functions 55

5.3．Congruences 59

5.4．The value at s=1 63

5.5．The p-adic regulator 70

5.6．Applications of the class number formula 77

CHAPTER 6 Stickelberger's Theorem 87

6.1．Gauss sums 87

6.2．Stickelberger's theorem 93

6.3．Herbrand's theorem 100

6.4．The index of the Stickeiberger ideal 102

6.5．Fermat's Last Theorem 107

CHAPTER 7 Iwasawa's Construction of p-adic L-functions 113

7.1．Group tings and power series 113

7.2．p-adic L-functions 117

7.3．Applications 125

7.4．Function fields 128

7.5．μ=0 130

CHAPTER 8 Cyclotomic Units 143

8.1．Cyclotomic units 143

8.2．Proof of the p-adic class number formula 151

8.3．Units of Q（ξp）and Vandiver's conjecture 153

8.4．p-adic expansions 159

CHAPTER 9 The Second Case of Fermat's Last Theorem 167

9.1．The basic argument 167

9.2．The theorems 173

CHAPrER 10 Galois Groups Acting on Ideal Class Groups 185

10.1．Some theorems on class groups 185

10.2．Reflection theorems 188

10.3．Consequences of Vandiver's conjecture 196

CHAPTER 11 Cyclotomic Fields of Class Numher One 205

11.1．The estimate for even characters 206

11.2．The estimate for all characters 211

11.3．The estimate for h- m 217

11.4．Odlyzko's bounds on discriminants 221

11.5．Calculation of h+ m 228

CHAPTER 12 Measures and Distributions 232

12.1．Distributions 232

12.2．Measures 237

12.3．Universal distributions 252

CHAPrER 13 Iwasawa's Theory of Zp-extensions 264

13.1．Basic facts 265

13.2．The structure of ？-modules 269

13.3．Iwasawa's theorem 277

13.4．Consequences 285

13.5．The maximal abelian p-extension unramified outside p 292

13.6．The main conjecture 297

13.7．Logarithmic derivatives 301

13.8．Local units modulo cyclotomic units 312

CHAPTER 14 The Kronecker-Weber Theorem 321

CHAPTER 15 The Main Conjecture and Annihilation of Class Groups 332

15.1．Stickelberger's theorem 332

15.2．Thaine's theorem 334

15.3．The converse of Herbrand's theorem 341

15.4．The Main Coniecture 348

15.5．Adjoints 351

15.6．Technical results from Iwasawa theory 360

15.7．Proof of the Main Conjecture 369

CHAPrER 16 Miscellany 373

16.1．Primality testing using Jaeobi sums 373

16.2．Sinnott's proof that μ=0 380

16.3．The non-p-part of the class number in a Zp-extension 385

Appendix 391

1．Inverse limits 391

2．Infinite Galois theory and ramification theory 392

3．Class field theory 396

Tables 407

1．Bernoulli numbers 407

2．Irregular primes 410

3．Relative class numbers 412

4．Real class numbers 420

Bibliography 424

List of Symbols 483

Index 485