group of principal ideles

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Takagi existence theorem — In class field theory, the Takagi existence theorem states that for any number field K there is a one to one inclusion reversing correspondence between the finite abelian extensions of K (in a fixed algebraic closure of K ) and the generalized… … Wikipedia
Hecke character — In mathematics, in the field of number theory, a Hecke character is a generalisation of a Dirichlet character, introduced by Erich Hecke to construct a class of L functions larger than Dirichlet L functions, and a natural setting for the Dedekind … Wikipedia
Algebraic number field — In mathematics, an algebraic number field (or simply number field) F is a finite (and hence algebraic) field extension of the field of rational numbers Q. Thus F is a field that contains Q and has finite dimension when considered as a vector… … Wikipedia
P-adic quantum mechanics — One may compute the energy levels for a potential well like this one.[note 1] P adic quantum mechanics is a relatively recent approach to understanding the nature of fundamental physics. It is the application of p adic analysis to quantum… … Wikipedia

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