Displaying similar documents to “On congruence modules associated to Λ -adic 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...

p -adic ordinary Hecke algebras for GL ( 2 )

Haruzo Hida (1994)

Annales de l'institut Fourier

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We study the p -adic nearly ordinary Hecke algebra for cohomological modular forms on G L ( 2 ) over an arbitrary number field F . We prove the control theorem and the independence of the Hecke algebra from the weight. Thus the Hecke algebra is finite over the Iwasawa algebra of the maximal split torus and behaves well under specialization with respect to weight and p -power level. This shows the existence and the uniqueness of the (nearly ordinary) p -adic analytic family of cohomological Hecke...