Displaying similar documents to “ p -adic L -functions for modular forms”

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.

p -adic L -functions of Hilbert modular forms

Andrzej Dabrowski (1994)

Annales de l'institut Fourier

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We construct p -adic L -functions (in general case unbounded) attached to “motivic" primitive Hilbert cusp forms as a non-archimedean Mellin transform of the corresponding admissible measure. In order to prove the growth conditions of the appropriate complex-valued distributions we represent them as Rankin type representation and use Atkin–Lehner theory and explicit form of Fourier coefficients of Eisenstein series.

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 , respectively. Define the Rankin product of f and g by 𝒟 N ( s , f , g ) = ( n = 1 ψ ξ ( n ) n k + - 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 ( + m , f , g ) π + 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...

Motives over totally real fields and p -adic L -functions

Alexei A. Panchishkin (1994)

Annales de l'institut Fourier

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Special values of certain L functions of the type L ( M , s ) are studied where M is a motive over a totally real field F with coefficients in another field T , and L ( M , s ) = 𝔭 L 𝔭 ( M , 𝒩 𝔭 - s ) is an Euler product 𝔭 running through maximal ideals of the maximal order 𝒪 F of F and L 𝔭 ( M , X ) - 1 = ( 1 - α ( 1 ) ( 𝔭 ) X ) · ( 1 - α ( 2 ) ( 𝔭 ) X ) · ... · ( 1 - α ( d ) ( 𝔭 ) X ) = 1 + A 1 ( 𝔭 ) X + ... + A d ( 𝔭 ) X d being a polynomial with coefficients in T . Using the Newton and the Hodge polygons of M one formulate a conjectural criterium for the existence of a p -adic analytic continuation of the special values....

On the image of Λ -adic Galois representations

Ami Fischman (2002)

Annales de l’institut Fourier

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We explore the question of how big the image of a Galois representation attached to a Λ -adic modular form with no complex multiplication is and show that for a “generic” set of Λ -adic modular forms (normalized, ordinary eigenforms with no complex multiplication), all have a large image.