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- Eichler–Shimura_congruence_relation abstract "In number theory, the Eichler–Shimura congruence relation expresses the local L-function of a modular curve at a prime p in terms of the eigenvalues of Hecke operators. It was introduced by Eichler (1954) and generalized by Shimura (1958). Roughly speaking, it says that the correspondence on the modular curve inducing the Hecke operator Tp is congruent mod p to the sum of the Frobenius map Frob and its transpose Ver. In other wordsTp = Frob + Ver as endomorphisms of the Jacobian J0(N)Fp of the modular curve X0N over the finite field Fp.The Eichler–Shimura congruence relation and its generalizations to Shimura varieties play a pivotal role in the Langlands program, by identifying a part of the Hasse–Weil zeta function of a modular curve or a more general modular variety with the product of Mellin transforms of weight 2 modular forms or a product of analogous automorphic L-functions.".
- Eichler–Shimura_congruence_relation wikiPageID "28167018".
- Eichler–Shimura_congruence_relation wikiPageRevisionID "597584743".
- Eichler–Shimura_congruence_relation subject Category:Modular_forms.
- Eichler–Shimura_congruence_relation subject Category:Zeta_and_L-functions.
- Eichler–Shimura_congruence_relation comment "In number theory, the Eichler–Shimura congruence relation expresses the local L-function of a modular curve at a prime p in terms of the eigenvalues of Hecke operators. It was introduced by Eichler (1954) and generalized by Shimura (1958). Roughly speaking, it says that the correspondence on the modular curve inducing the Hecke operator Tp is congruent mod p to the sum of the Frobenius map Frob and its transpose Ver.".
- Eichler–Shimura_congruence_relation label "Eichler–Shimura congruence relation".
- Eichler–Shimura_congruence_relation sameAs Eichler%E2%80%93Shimura_congruence_relation.
- Eichler–Shimura_congruence_relation sameAs Q5348729.
- Eichler–Shimura_congruence_relation sameAs Q5348729.
- Eichler–Shimura_congruence_relation wasDerivedFrom Eichler–Shimura_congruence_relation?oldid=597584743.