Hecke characters
E839483
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.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Hecke characters canonical | 3 |
How this entity was disambiguated
This entity first appeared as the object of triple T10061988 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Hecke characters Context triple: [Hilbert’s twelfth problem, involves, Hecke characters]
-
A.
Hecke operators
Hecke operators are algebraic operators acting on modular forms that play a central role in number theory, particularly in understanding congruences, L-functions, and the arithmetic of modular forms.
-
B.
Dirichlet characters
Dirichlet characters are completely multiplicative periodic arithmetic functions modulo an integer, fundamental in analytic number theory for constructing Dirichlet L-functions and studying the distribution of primes in arithmetic progressions.
-
C.
Dedekind zeta functions
Dedekind zeta functions are number-theoretic functions attached to algebraic number fields that encode their arithmetic properties, such as the distribution of prime ideals and class numbers.
-
D.
Hecke theory
Hecke theory is a branch of number theory centered on Hecke operators and modular forms, providing powerful tools to study arithmetic properties of modular forms and related objects.
-
E.
Dirichlet L-functions
Dirichlet L-functions are complex analytic functions built from Dirichlet characters that generalize the Riemann zeta function and play a central role in number theory, particularly in the study of primes in arithmetic progressions.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Hecke characters Target entity description: 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.
-
A.
Hecke operators
Hecke operators are algebraic operators acting on modular forms that play a central role in number theory, particularly in understanding congruences, L-functions, and the arithmetic of modular forms.
-
B.
Dirichlet characters
Dirichlet characters are completely multiplicative periodic arithmetic functions modulo an integer, fundamental in analytic number theory for constructing Dirichlet L-functions and studying the distribution of primes in arithmetic progressions.
-
C.
Dedekind zeta functions
Dedekind zeta functions are number-theoretic functions attached to algebraic number fields that encode their arithmetic properties, such as the distribution of prime ideals and class numbers.
-
D.
Hecke theory
Hecke theory is a branch of number theory centered on Hecke operators and modular forms, providing powerful tools to study arithmetic properties of modular forms and related objects.
-
E.
Dirichlet L-functions
Dirichlet L-functions are complex analytic functions built from Dirichlet characters that generalize the Riemann zeta function and play a central role in number theory, particularly in the study of primes in arithmetic progressions.
- F. None of above. chosen
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
ⓘ
Hecke L-functions ⓘ
linked to:
L-functions
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
ⓘ
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 ⓘ |
| playRoleIn |
description of abelian extensions of number fields
ⓘ
functional equations of L-functions ⓘ proofs of analytic continuation of L-functions ⓘ |
| relatedTo |
Grössencharacters of Weil
ⓘ
linked to:
Weil group
automorphic representations of GL(1) ⓘ idele class characters of global fields ⓘ |
| restrictTo | idele group of Q to give Dirichlet characters ⓘ |
| usedIn |
Artin reciprocity
ⓘ
linked to:
Artin reciprocity law
Langlands program ⓘ class field theory ⓘ construction of Hecke L-functions ⓘ study of L-functions ⓘ |
| usedToDefine |
Grössencharakter L-functions
ⓘ
linked to:
Grössencharaktere of number fields
Hecke L-series ⓘ
linked to:
L-functions
|
How these facts were elicited
The pipeline generated the facts above by prompting gpt-5.1 with this entity's name + description and the instruction below.
Instruction
You are a knowledge base construction expert. Given a subject entity and a description of it, return factual statements that you know for the subject as a JSON list of dictionaries(triples), where keys must be "subject", "predicate" and "object". The number of facts may be very high, between 25 to 50 or more, for very popular subjects. For less popular subjects, the number of facts can be very low, like 5 or 10. # Requirements - If you don't know the subject at all, return an empty list. - If the subject is not a named entity, return an empty list. - Include at least one triple where predicate is "instanceOf". - Do not get too wordy. - Separate several objects into multiple triples with one object.
Input
Subject: Hecke characters Description of subject: 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.
Referenced by (3)
Full triples — surface form annotated when it differs from this entity's canonical label.