Shimura correspondence
E1281164
UNEXPLORED
The Shimura correspondence is a fundamental result in number theory that establishes a deep link between modular forms of half-integral weight and modular forms of integral weight, with important applications to L-functions and arithmetic geometry.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Shimura correspondence canonical | 3 |
How this entity was disambiguated
This entity first appeared as the object of triple T17671609 — 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: Shimura correspondence Context triple: [Goro Shimura, knownFor, Shimura correspondence]
-
A.
Shimura varieties
Shimura varieties are higher-dimensional algebraic varieties that generalize modular curves and play a central role in the Langlands program by connecting number theory, automorphic forms, and arithmetic geometry.
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B.
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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C.
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.
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D.
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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E.
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.
- 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: Shimura correspondence Target entity description: The Shimura correspondence is a fundamental result in number theory that establishes a deep link between modular forms of half-integral weight and modular forms of integral weight, with important applications to L-functions and arithmetic geometry.
-
A.
Shimura varieties
Shimura varieties are higher-dimensional algebraic varieties that generalize modular curves and play a central role in the Langlands program by connecting number theory, automorphic forms, and arithmetic geometry.
-
B.
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.
-
C.
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.
-
D.
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.
-
E.
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.
- F. None of above. chosen
Referenced by (3)
Full triples — surface form annotated when it differs from this entity's canonical label.