Displaying similar documents to “ p -adic measures attached to Siegel modular forms”

Congruences among modular forms on U(2,2) and the Bloch-Kato conjecture

Krzysztof Klosin (2009)

Annales de l’institut Fourier

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Let k be a positive integer divisible by 4, p > k a prime, f an elliptic cuspidal eigenform (ordinary at p ) of weight k - 1 , level 4 and non-trivial character. In this paper we provide evidence for the Bloch-Kato conjecture for the motives ad 0 M ( - 1 ) and ad 0 M ( 2 ) , where M is the motif attached to f . More precisely, we prove that under certain conditions the p -adic valuation of the algebraic part of the symmetric square L -function of f evaluated at k provides a lower bound for the p -adic valuation of the order...

p -adic interpolation of convolutions of Hilbert modular forms

Volker Dünger (1997)

Annales de l'institut Fourier

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In this paper we construct p -adic measures related to the values of convolutions of Hilbert modular forms of integral and half-integral weight at the negative critical points under the assumption that the underlying totally real number field F has class number h F = 1 . This extends the result of Panchishkin [Lecture Notes in Math., 1471, Springer Verlag, 1991 ] who treated the case that both modular forms are of integral weight. In order to define the measures, we need to introduce the twist...

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....

Jacobi-Eisenstein series and p -adic interpolation of symmetric squares of cusp forms

Pavel I. Guerzhoy (1995)

Annales de l'institut Fourier

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The aim of this paper is to construct and calculate generating functions connected with special values of symmetric squares of modular forms. The Main Theorem establishes these generating functions to be Jacobi-Eisenstein series i.e. Eisenstein series among Jacobi forms. A theorem on p -adic interpolation of the special values of the symmetric square of a p -ordinary modular form is proved as a corollary of our Main Theorem.