Algebraic Number TheoryFrom 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
Risultati 1-5 di 5
Pagina 8
Chapter 1 Basic Number Theory The first goal of algebraic number theory is the
generalization of the theorem on the unique representation of natural numbers as
products of prime numbers to algebraic numbers. Gauss considered the ring ...
Chapter 1 Basic Number Theory The first goal of algebraic number theory is the
generalization of the theorem on the unique representation of natural numbers as
products of prime numbers to algebraic numbers. Gauss considered the ring ...
Pagina 9
By arithmetic in Z we mean the unique factorization of natural numbers in the
product of prime numbers. The arithmetic in Q is given by the arithmetic in Z: Any
re Q – {0} has a uniquely determined representation r = (–1) II p” p where the ...
By arithmetic in Z we mean the unique factorization of natural numbers in the
product of prime numbers. The arithmetic in Q is given by the arithmetic in Z: Any
re Q – {0} has a uniquely determined representation r = (–1) II p” p where the ...
Pagina 22
3) Let K be an algebraic number field and C an order in K. In this paragraph we
consider the problem of generalization of the unique factorization of natural
numbers in products of prime numbers. We will see that this is possible in a
satisfying ...
3) Let K be an algebraic number field and C an order in K. In this paragraph we
consider the problem of generalization of the unique factorization of natural
numbers in products of prime numbers. We will see that this is possible in a
satisfying ...
Pagina 49
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Pagina 60
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Sommario
| 7 | |
| 19 | |
3 Dedekind Rings | 28 |
4 Valuations | 45 |
5 Harmonic Analysis on Local and Global Fields | 63 |
6 Hecke LSeries and the Distribution of Prime Ideals | 70 |
Class Field Theory | 90 |
2 Complex Multiplication | 107 |
2 Galois Cohomology of Local and Global Fields | 168 |
Abelian Fields | 192 |
3 Iwasawas Theory of IExtensions | 206 |
4 padic LFunctions | 212 |
Artin LFunctions and Galois Module Structure | 219 |
2 Galois Module Structure and Artin Root Numbers | 234 |
Fields Domains and Complexes | 237 |
Tables | 245 |
5 Simple Algebras | 131 |
6 Explicit Reciprocity Laws and Symbols | 137 |
7 Further Results of Class Field Theory | 145 |
Cohomology of Profinite Groups | 151 |
References | 251 |
Author Index 263 | 262 |
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Parole e frasi comuni
abelian extension algebraic number field arbitrary Artin basis called Chap character class field theory class group class number closed complex compute conductor conjecture consider contains continuous corresponding cyclic cyclic extension cyclotomic defined definition denotes determined direct discriminant divisor elements embedding equal equation exact Example exists factor finite finite extension fixed formula function Furthermore G-module Galois group given global group G Hence Hilbert homomorphism implies induces infinite integers irreducible isomorphism L-functions Let G Let L/K Main reference maximal means module morphism multiplication natural number norm normal extension p-adic places polynomial prime ideal principal problem profinite group Proof properties Proposition proved quadratic ramified representation residue respect restriction ring roots of unity sequence shows structure subgroup symbol Theorem trivial unique unit unramified valuation values
Informazioni bibliografiche
| Titolo | Algebraic Number Theory Volume 62 di Encyclopaedia of Mathematical Sciences |
| Autore | H. Koch |
| Curatori | A.N. Parshin, I.R. Shafarevich |
| Edizione | illustrata |
| Editore | Springer Science & Business Media, 2012 |
| ISBN | 3642580955, 9783642580956 |
| Lunghezza | 269 pagine |
| Esporta citazione | BiBTeX EndNote RefMan |