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Algebraic Number Theory : Encyclopaedia of Mathematical Sciences - H. Koch

Algebraic Number Theory

Encyclopaedia of Mathematical Sciences

By: H. Koch, A.N. Parshin (Editor), I. R. Shafarevich (Editor)

Paperback Published: 12th September 1997
ISBN: 9783540630036
Number Of Pages: 269

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From the reviews: ..". The author succeeded in an excellent way to describe the various points of view under which Class Field Theory can be seen. ... In any case the author succeeded to write a very readable book on these difficult themes." Monatshefte fuer Mathematik, 1994
..". Number theory is not easy and quite technical at several places, as the author is able to show in his technically good exposition. The amount of difficult material well exposed gives a survey of quite a lot of good solid classical number theory... Conclusion: for people not already familiar with this field this book is not so easy to read, but for the specialist in number theory this is a useful description of (classical) algebraic number theory." Medelingen van het wiskundig genootschap, 1995

From the reviews: ..". The author succeeded in an excellent way to describe the various points of view under which Class Field Theory can be seen. ... In any case the author succeeded to write a very readable book on these difficult themes." Monatshefte fuer Mathematik, 1994 ..". Number theory is not easy and quite technical at several places, as the author is able to show in his technically good exposition. The amount of difficult material well exposed gives a survey of quite a lot of good solid classical number theory... Conclusion: for people not already familiar with this field this book is not so easy to read, but for the specialist in number theory this is a useful description of (classical) algebraic number theory." Medelingen van het wiskundig genootschap, 1995

Prefacep. 7
Basic Number Theoryp. 8
Orders in Algebraic Number Fieldsp. 9
Rings with Divisor Theoryp. 22
Dedekind Ringsp. 27
Valuationsp. 45
Harmonic Analysis on Local and Global Fieldsp. 63
Hecke L-Series and the Distribution of Prime Idealsp. 70
Class Field Theoryp. 90
The Main Theorems of Class Field Theoryp. 92
Complex Multiplicationp. 107
Cohomology of Groupsp. 112
Proof of the Main Theorems of Class Field Theoryp. 121
Simple Algebrasp. 131
Explicit Reciprocity Laws and Symbolsp. 137
Further Results of Class Field Theoryp. 145
Galois Groupsp. 150
Cohomology of Profinite Groupsp. 151
Galois Cohomology of Local and Global Fieldsp. 168
Extensions with Given Galois Groupsp. 182
Abelian Fieldsp. 192
The Integers of an Abelian Fieldp. 193
The Arithmetical Class Number Formulap. 195
Iwasawa's Theory of [Gamma]-Extensionsp. 206
p-adic L-Functionsp. 211
Artin L-Functions and Galois Module Structurep. 219
Artin L-Functionsp. 222
Galois Module Structure and Artin Root Numbersp. 234
Fields, Domains, and Complexesp. 237
Quadratic Residuesp. 240
Locally Compact Groupsp. 241
Bernoulli Numbersp. 243
Tablesp. 245
Referencesp. 251
Author Indexp. 263
Subject Indexp. 266
Table of Contents provided by Blackwell. All Rights Reserved.

ISBN: 9783540630036
ISBN-10: 3540630031
Series: Encyclopaedia of Mathematical Sciences
Audience: General
Format: Paperback
Language: English
Number Of Pages: 269
Published: 12th September 1997
Publisher: Springer-Verlag Berlin and Heidelberg Gmbh & Co. Kg
Country of Publication: DE
Dimensions (cm): 23.72 x 15.52  x 1.65
Weight (kg): 0.41

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