Displaying similar documents to “The p -adic measure on the orbit of an element of p

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...

A representation theorem for a class of rigid analytic functions

Victor Alexandru, Nicolae Popescu, Alexandru Zaharescu (2003)

Journal de théorie des nombres de Bordeaux

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Let p be a prime number, p the field of p -adic numbers and p the completion of the algebraic closure of p . In this paper we obtain a representation theorem for rigid analytic functions on 𝐏 1 ( p ) C ( t , ϵ ) which are equivariant with respect to the Galois group G = G a l c o n t ( p / p ) , where t is a lipschitzian element of p and C ( t , ϵ ) denotes the ϵ -neighborhood of the G -orbit of t .