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- Q5348729 subject Q7029575.
- Q5348729 subject Q7139612.
- Q5348729 subject Q9243089.
- Q5348729 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 words,Tp = 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.".
- Q5348729 wikiPageWikiLink Q12479.
- Q5348729 wikiPageWikiLink Q1393253.
- Q5348729 wikiPageWikiLink Q1592959.
- Q5348729 wikiPageWikiLink Q190524.
- Q5348729 wikiPageWikiLink Q2372257.
- Q5348729 wikiPageWikiLink Q3001220.
- Q5348729 wikiPageWikiLink Q3075294.
- Q5348729 wikiPageWikiLink Q353411.
- Q5348729 wikiPageWikiLink Q49008.
- Q5348729 wikiPageWikiLink Q606934.
- Q5348729 wikiPageWikiLink Q7029575.
- Q5348729 wikiPageWikiLink Q7139612.
- Q5348729 wikiPageWikiLink Q718045.
- Q5348729 wikiPageWikiLink Q7497063.
- Q5348729 wikiPageWikiLink Q769124.
- Q5348729 wikiPageWikiLink Q870797.
- Q5348729 wikiPageWikiLink Q9243089.
- Q5348729 type Thing.
- Q5348729 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.".
- Q5348729 label "Eichler–Shimura congruence relation".
- Q5348729 differentFrom Q5348730.