Algebraic Number Theory

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Springer Science & Business Media, 6 dic 2012 - 269 pagine
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

Dall'interno del libro

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Sommario

Preface
7
2 Rings with Divisor Theory
22
3 Dedekind Rings
28
60
42
69
49
76
56
Harmonic Analysis on Local and Global Fields
63
6 Hecke LSeries and the Distribution of Prime Ideals
70
7 Further Results of Class Field Theory
145
Cohomology of Profinite Groups
151
2 Galois Cohomology of Local and Global Fields
168
Abelian Fields
192
3 Iwasawas Theory of IExtensions
206
Artin LFunctions and Galois Module Structure
219
2 Galois Module Structure and Artin Root Numbers
234
Fields Domains and Complexes
237

Class Field Theory
90
2 Complex Multiplication
107
Simple Algebras
131
6 Explicit Reciprocity Laws and Symbols
137
Tables
245
References
251
Author Index 263
262
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