10.1007/978-3-662-03983-0

Neukirch, J. (1999). 10.1007/978-3-662-03983-0. Algebraic Number Theory.

Type

Book

Intellectual base

Review or monograph

Year

1999

DOI

10.1007/978-3-662-03983-0

ISBN

9783642084737

Link

https://doi.org/10.1007/978-3-662-03983-0

Cited by

4 citations across 4 artifacts.

Each citation links to the sentence it supports in the citing article.

Domain-specific

• Algebraic number field
  • An algebraic number field is a field extension K/Q of finite degree, equivalently a field generated over Q by finitely many algebraic numbers and, by the primitive element theorem in characteristic zero, by one algebraic number.
• Dedekind zeta function
  • The Dedekind zeta function is ζ_K(s)=Σ_{I≠0}N(I)^{-s}, initially for Re(s)>1, equivalently an Euler product over prime ideals.
• Hecke Character
  • Its values on uniformizers generate an Euler product and Hecke L-function, extending Dirichlet L-functions from \(\mathbb Q\) to general number fields.
• Profinite Integer
  • The absolute Galois group of a finite field is canonically isomorphic to \(\widehat{\mathbb Z}\) as a profinite group, with Frobenius supplying a topological generator in the procyclic sense.

    This sourceReference for local fields, Galois groups, and arithmetic completions.

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