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Books, Free Shipping, Cyclotomic Fields

Posted at: Offers to Sell and Export | Posted on: Fri 30 Jul, 2010 9:32 am | Product Category: Reference books [3760]
 
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Product Details

Author Lang.S


Publisher World Publishing Corporation

Isbn 9787510004773, 7510004772

Published

June 2009

Pages 433

Size 24k

Edition First

Format Paperback

Language English

Page material gelatine plate paper

Product Description:

Kummer's work on cyclotomic fields paved the way for the development ofalgebraic number theory in general by Dedekind, Weber, Hensel, Hilbert, Takagi, Artin and others. However, the success of this general theory hastended to obscure special facts proved by Kummer about cyclotomic fieldswhich lie deeper than the general theory. For a long period in the 20th centurythis aspect of Kummer's work seems to have been largely forgotten, exceptfor a few papers, among which are those by Pollaczek [Po], Artin-Hasse[A-H] and Vandiver . In the mid 1950's, the theory of cyclotomic fields was taken up again byIwasawa and Leopoldt. Iwasawa viewed cyclotomic fields as being analoguesfor number fields of the constant field extensions of algebraic geometry, andwrote a great sequence of papers investigating towers of cyclotomic fields, and more generally, Gaiois extensions of number fields whose Galois groupis isomorphic to the additive group ofp-adic integers. Leopoldt concentratedon a fixed cyclotomic field, and established various p-adic analogues of theclassical complex analytic

Contents:

Notation

Introduction

CHAPTER 1 Character Sums

 1.Character Sums over Finite Fields

 2.Stickelberger's Theorem

 3.Relations in the Ideal Classes

 4.Jacobi Sumsas Hecke Characters

 5.Gauss Sums over Extension Fields

 6.Application to the Fermat Curve

CHAPTER 2 Stickelberger Ideals and Bernoulli Distribution

 1.The Index of the First Stickelberger Ideal

 2.Bernoulli Numbers

 3.Integral Stickelberger Ideals

 4.General Comments on Indices

 5.The Index for k Even

 6.The Index for k Odd

 7.Twistings and Stickelberger Ideals

 8.Stickelberger Elements as Distributions

 9.Universal Distributions

 10. The Davenport-Hasse Distribution

Appendix. Distributions

CHAPTER 3 Complex Analytic Class Number Formulas

 1.Gauss Sums on Z/raZ

 2.Primitive L-series

 3.Decomposition of L-series

 4.The (+ I)-eigenspaces

 5.Cyclotomic Units

 6.The Dedekind Determinant

 7.Bounds for Class Numbers

CHAPTER 4 The p-adic L-function

CHAPTER 5 Iwasawa Theory and Ideal Class Groups

CHAPTER 6 Kummer Theory over Cyclotomic Zextensions

CHAPTER 7 Iwasawa Theory of Local Units

……



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