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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
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- (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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