Hecke characters

E839483

Grössencharaktere generalized Dirichlet characters idele class characters mathematical concept

Hecke characters are generalized algebraic number field characters (or Grössencharaktere) that play a central role in class field theory and the study of L-functions.

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Statements (47)

Predicate	Object
instanceOf	Grössencharaktere ⓘ generalized Dirichlet characters ⓘ idele class characters ⓘ mathematical concept ⓘ
appearIn	Hecke’s theory of modular forms and L-functions ⓘ construction of Grossencharacter motives ⓘ proofs of class number formulas ⓘ study of CM (complex multiplication) elliptic curves ⓘ
are	continuous homomorphisms from the idele class group to C× ⓘ
associatedWith	Grössencharaktere of number fields NERFINISHED ⓘ Hecke L-functions NERFINISHED ⓘ idele class group ⓘ ray class groups ⓘ
canBe	quasi-characters of the idele class group ⓘ
canBeViewedAs	characters of ray class groups via global class field theory ⓘ
codomain	multiplicative group of complex numbers ⓘ
definedOn	idele class group of a number field ⓘ idele group of a number field ⓘ
domain	idele class group ⓘ
field	algebraic number theory ⓘ analytic number theory ⓘ class field theory ⓘ
generalize	Dirichlet characters NERFINISHED ⓘ ray class characters ⓘ
haveInvariant	conductor ⓘ infinity type ⓘ ramification data ⓘ
haveType	algebraic Hecke characters ⓘ finite order Hecke characters ⓘ ramified Hecke characters ⓘ unitary Hecke characters ⓘ unramified Hecke characters ⓘ
namedAfter	Erich Hecke NERFINISHED ⓘ
playRoleIn	description of abelian extensions of number fields ⓘ functional equations of L-functions ⓘ proofs of analytic continuation of L-functions ⓘ
relatedTo	Grössencharacters of Weil NERFINISHED ⓘ automorphic representations of GL(1) ⓘ idele class characters of global fields ⓘ
restrictTo	idele group of Q to give Dirichlet characters ⓘ
usedIn	Artin reciprocity NERFINISHED ⓘ Langlands program NERFINISHED ⓘ class field theory ⓘ construction of Hecke L-functions ⓘ study of L-functions ⓘ
usedToDefine	Grössencharakter L-functions NERFINISHED ⓘ Hecke L-series NERFINISHED ⓘ

Referenced by (1)

Full triples — surface form annotated when it differs from this entity's canonical label.

Hilbert’s twelfth problem → involves → Hecke characters ⓘ