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