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Congruences among modular forms on U(2,2) and the Bloch-Kato conjecture

Krzysztof Klosin (2009)

Annales de l’institut Fourier

Let k be a positive integer divisible by 4, p > k a prime, f an elliptic cuspidal eigenform (ordinary at p ) of weight k - 1 , level 4 and non-trivial character. In this paper we provide evidence for the Bloch-Kato conjecture for the motives ad 0 M ( - 1 ) and ad 0 M ( 2 ) , where M is the motif attached to f . More precisely, we prove that under certain conditions the p -adic valuation of the algebraic part of the symmetric square L -function of f evaluated at k provides a lower bound for the p -adic valuation of the order of the Pontryagin...

Congruences modulo between ϵ factors for cuspidal representations of G L ( 2 )

Marie-France Vignéras (2000)

Journal de théorie des nombres de Bordeaux

Let p be two different prime numbers, let F be a local non archimedean field of residual characteristic p , and let 𝐐 ¯ , 𝐙 ¯ , 𝐅 ¯ be an algebraic closure of the field of -adic numbers 𝐐 , the ring of integers of 𝐐 ¯ , the residual field of 𝐙 ¯ . We proved the existence and the unicity of a Langlands local correspondence over 𝐅 ¯ for all n 2 , compatible with the reduction modulo in [V5], without using L and ϵ factors of pairs. We conjecture that the Langlands local correspondence over 𝐐 ¯ respects congruences modulo between...

Eisenstein series and Poincaré series for mixed automorphic forms.

Min Ho Lee (2000)

Collectanea Mathematica

Mixed automorphic forms generalize elliptic modular forms, and they occur naturally as holomorphic forms of the highest degree on families of abelian varieties parametrized by a Riemann surface. We construct generalized Eisenstein series and Poincaré series, and prove that they are mixed automorphic forms.

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