Hecke eigenvalues
E1318601
UNEXPLORED
Hecke eigenvalues are the scalar values by which Hecke operators act on eigenforms or automorphic forms, encoding deep arithmetic information such as Fourier coefficients and connections to L-functions.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Hecke eigenvalues canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T18299095 — 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 eigenvalues Context triple: [Hecke operators, usedToDefine, Hecke eigenvalues]
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A.
Hecke eigenforms
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.
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B.
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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C.
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.
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D.
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.
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E.
Deligne bound for Fourier coefficients of modular forms
The Deligne bound for Fourier coefficients of modular forms is a deep result in number theory, proved by Pierre Deligne, that gives optimal size estimates for the Fourier coefficients of cusp forms and confirms the Ramanujan–Petersson conjecture for modular forms.
- 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 eigenvalues Target entity description: Hecke eigenvalues are the scalar values by which Hecke operators act on eigenforms or automorphic forms, encoding deep arithmetic information such as Fourier coefficients and connections to L-functions.
-
A.
Hecke eigenforms
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.
-
B.
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.
-
C.
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.
-
D.
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.
-
E.
Deligne bound for Fourier coefficients of modular forms
The Deligne bound for Fourier coefficients of modular forms is a deep result in number theory, proved by Pierre Deligne, that gives optimal size estimates for the Fourier coefficients of cusp forms and confirms the Ramanujan–Petersson conjecture for modular forms.
- F. None of above. chosen
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.