Displaying similar documents to “Quantizations and symbolic calculus over the p -adic numbers”

On p -adic L -functions of G L ( 2 ) × G L ( 2 ) over totally real fields

Haruzo Hida (1991)

Annales de l'institut Fourier

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Let D ( s , f , g ) be the Rankin product L -function for two Hilbert cusp forms f and g . This L -function is in fact the standard L -function of an automorphic representation of the algebraic group G L ( 2 ) × G L ( 2 ) defined over a totally real field. Under the ordinarity assumption at a given prime p for f and g , we shall construct a p -adic analytic function of several variables which interpolates the algebraic part of D ( m , f , g ) for critical integers m , regarding all the ingredients m , f and g as variables.

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...