Displaying similar documents to “On p -adic L -functions of G L ( 2 ) × G L ( 2 ) over totally real fields”

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...

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.

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...

Endomorphism algebras of motives attached to elliptic modular forms

Alexander F. Brown, Eknath P. Ghate (2003)

Annales de l’institut Fourier

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We study the endomorphism algebra of the motive attached to a non-CM elliptic modular cusp form. We prove that this algebra has a sub-algebra isomorphic to a certain crossed product algebra X . The Tate conjecture predicts that X is the full endomorphism algebra of the motive. We also investigate the Brauer class of X . For example we show that if the nebentypus is real and p is a prime that does not divide the level, then the local behaviour of X at a place lying above p is essentially...