Displaying similar documents to “Iwasawa modules attached to congruences of cusp forms”

A p -adic measure attached to the zeta functions associated with two elliptic modular forms. II

Haruzo Hida (1988)

Annales de l'institut Fourier

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Let f = ∑ n = 1 ∞ a ( n ) q n and g = ∑ n = 1 ∞ b ( n ) q n be holomorphic common eigenforms of all Hecke operators for the congruence subgroup Γ 0 ( N ) of S L 2 ( Z ) with “Nebentypus” character ψ and ξ and of weight k and ℓ , respectively. Define the Rankin product of f and g by 𝒟 N ( s , f , g ) = ( ∑ n = 1 ∞ ψ ξ ( n ) n k + ℓ - 2 s - 2 ) ( ∑ n = 1 ∞ a ( n ) b ( n ) n - s ) . Supposing f and g to be ordinary at a prime p ≥ 5 , we shall construct a p -adically analytic L -function of three variables which interpolate the values 𝒟 N ( ℓ + m , f , g ) π ℓ + 2 m + 1 < f , f > for integers m with 0 ≤ m < k - 1 , by regarding all the ingredients m , f and g as variables. Here ⟨ f , f ⟩ is the Petersson...

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

Krzysztof Klosin (2009)

Annales de l’institut Fourier

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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...