割圆域导论（第2版）（英文版）
作者： (美)华盛顿
出版时间：2014年7月
出版社：世界图书出版公司
- 世界图书出版公司
- 9787510077852
- 38458
- 2014年7月
- 未分类
- 未分类
- O156
华盛顿所著的《割圆域导论（第2版）（英文版）》是一部讲述数论很重要领域的教程，包括p进数L—函数、类数、割圆单元、费马最后定理和Z—p扩展Iwasawa定理。这是第二版，新增加了许多内容，如Thaine，Kolyvagin，andRubin的著作、主猜想的证明，以及一章最新其他进展。目次：费曼大定理；基本结果；狄里克莱性质；狄里克莱L级数和类数公式；p进数和伯努利数；Stickelberger定理；p进数L—函数的Iwasawa结构；割圆单元；费曼大定理第二案例；伽罗瓦群作用于理想类群上；类数1的割圆域；测度与分布。
Preface to the Second Edition
Preface to the First Edition
CHAPTER I
Fermat's Last Theorem
CHAPTER 2
Basic Results
CHAPTER 3
Dirichlet Characters
CHAPTER 4
Dirichlet L-series and Class Number Formulas
CHAPTER 5
p-adic L-functions and Bernoulli Numbers
5.1. p-adic functions
5.2. p-adic L-functions
5.3. Congruences
5.4. The value at s = 1
5.5. The p-adic regulator
5.6. Applications of the class number formula
CHAPTER 6
Stickelberger's Theorem
6.1. Gauss sums
6.2. Stickelberger's theorem
6.3. Herbrand's theorem
6.4. The index of the Stickelberger ideal
6.5. Fermat's Last Theorem
CHAPTER 7
lwasawa's Construction of p-adic L-functions
7.1. Group rings and power series
7.2. p-adic L-functions
7.3. Applications
7.4. Function fields
7.5. μ=O
CHAPTER 8
Cyclotomic Units
8.1. Cyclotomic units
8.2. Proof of the p-adic class number formula
8.3. Units of O(Cp) and Vandiver's conjecture
8.4. p-adic expansions
CHAPTER 9
The Second Case of Fermat's Last Theorem
9.1. The basic argument
9.2. The theorems
CHAPTER 10
Galois Groups Acting on Ideal Class Groups
10.1. Some theorems on class groups
10.2. Reflection theorems
10.3. Consequences of Vandiver's conjecture
CHAPTER I 1
Cyclotomic Fields of Class Number One
11.1. The estimate for even characters
l1.2. The estimate for all characters
11.3. The estimate for hm,
11.4. Odlyzko's bounds on discriminants
11.5. Calculation of hm+
CHAPTER 12
Measures and Distributions
12.1. Distributions
12.2. Measures
12.3. Universal distributions
CHAPTER 13
Iwasawa's Theory of Zp-extensions
13.1. Basic facts
13.2. The structure of A-modules
13.3. Iwasawa's theorem
13.4. Consequences
13.5. The maximal abelian p-extension unramifiexl outside p
13.6. The main conjecture
13.7. Logarithmic derivatives
13.8. Local units modulo cyclotomi~ units
CHAPTER 14
The Kronecker-Weber Theorem
CHAPTER 15
The Main Conjecture and Annihilation of Class Groups
15.1. Stickelberger's theorem
15.2. Thaine's theorem
15.3. The converse of Herbrand's theorem
15.4. The Main Conjecture
15.5. Adjoints
15.6. Technical results from Iwasawa theory
15.7. Proof of the Main Conjecture
CHAPTER 16
Misccllany
16.1. Primality testing using Jacobi sums
16.2. Sinnott's proof thatμ= 0
16.3. The non-p-part of the class number in a Zp-extension
Appendix
1. Inverse limits
2. Infinite Galois theory and ramification theory
3. Class field theory
Tables
1. Bernoulli numbers
2. Irregular primes
3. Relative class numbers
4. Real class numbers
Bibliography
List of Symbols
Index
