Hecke eigenforms
E1094042
UNEXPLORED
Hecke eigenforms are special modular forms that are simultaneous eigenfunctions of all Hecke operators, playing a central role in modern number theory and the theory of automorphic forms.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Hecke eigenforms canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T14334568 — 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 eigenforms Context triple: [Ramanujan–Petersson conjecture, concerns, Hecke eigenforms]
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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.
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B.
Automorphic Forms and Representations
Automorphic Forms and Representations is a foundational mathematical monograph that develops the theory of automorphic forms and their connections to representation theory and number theory.
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C.
Hecke characters
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.
-
D.
Euler products for automorphic L-functions
Euler products for automorphic L-functions are infinite product expansions attached to automorphic representations that encode deep arithmetic information and generalize the classical Euler product of the Riemann zeta function to a broad class of L-functions in the Langlands program.
-
E.
Eisenstein series
Eisenstein series are special types of complex analytic functions on the upper half-plane (or more general symmetric spaces) that play a central role in the theory of modular and automorphic forms, connecting number theory, representation theory, and harmonic analysis.
- 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 eigenforms Target entity description: Hecke eigenforms are special modular forms that are simultaneous eigenfunctions of all Hecke operators, playing a central role in modern number theory and the theory of automorphic forms.
-
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.
Automorphic Forms and Representations
Automorphic Forms and Representations is a foundational mathematical monograph that develops the theory of automorphic forms and their connections to representation theory and number theory.
-
C.
Hecke characters
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.
-
D.
Euler products for automorphic L-functions
Euler products for automorphic L-functions are infinite product expansions attached to automorphic representations that encode deep arithmetic information and generalize the classical Euler product of the Riemann zeta function to a broad class of L-functions in the Langlands program.
-
E.
Eisenstein series
Eisenstein series are special types of complex analytic functions on the upper half-plane (or more general symmetric spaces) that play a central role in the theory of modular and automorphic forms, connecting number theory, representation theory, and harmonic analysis.
- F. None of above. chosen
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.