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割圆域引论·第2版（英文版）

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作者：L.C.Washington 著著

出版社：世界图书出版公司

出版时间：2003-6-1

I S B N：9787506260022

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割圆域引论第2版

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割圆域引论·第2版（英文版）

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内容简介

Since the publication of the first edition, several remarkable developments have taken place. The work of Thaine, Kolyvagin, and Rubin has produced fairly elementary proofs of Ribet's converse of Herbrand's theorem and of the Main Conjecture. The original proofs of both of these results used delicate techniques from algebraic geometry and were inaccessible to many readers. Also, Sinnott discovered a beautiful proof of the vanishing of Iwasawa's u-invariant that is much simpler than the one given in Chapter 7. Finally, Fermat's Last Theorem was proved by Wiles, using work of Frey, Ribet, Serre, Mazur, Langlands-Tunnell, Taylor-Wiles, and others. Although the proof, which is based on modular forms and elliptic curves, is much different from the cyclotomic approaches described in this book, several of the ingredients were inspired by ideas from cyclotomic fields and Iwasawa theory.

作者简介

Preface to the Second Edition
Preface to the First Edition
CHAPTER 1 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
CHAPTER 7 Iwasawa's Construction of p-adic L-function
CHAPTER 8 Cyclotomic Units
CHAPTER 9 The Second Case of Fermat's Last Theorm
CHAPTER 10 Galois Groups Acting on Ideal Class Groups
CHAPTER 11 Cyclotomic Fields of Class Number One
CHAPTER 12 Measures and Distribution
CHAPTER 13 Iwasawa's Theory of Zp-extensions
CHAPTER 14 The Kronecker-Weber Theorem
CHAPTER 15 The Main Conjecture and Annihilation of Class Groups
CHAPTER 16 Misscellany
Appendix
Tables
Bibliography
List of Symbols
Index