Admissible -adic measures attached to triple products of elliptic cusp forms.

Böcherer, Siegfried; Panchishkin, A.A.

Displaying similar documents to “Admissible $p$ -adic measures attached to triple products of elliptic cusp forms.”

$p$ -adic measures attached to Siegel modular forms

Siegfried Böcherer, Claus-Günther Schmidt (2000)

Annales de l'institut Fourier

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We study the critical values of the complex standard- $L$ -function attached to a holomorphic Siegel modular form and of the twists of the $L$ -function by Dirichlet characters. Our main object is for a fixed rational prime number $p$ to interpolate $p$ -adically the essentially algebraic critical $L$ -values as the Dirichlet character varies thus providing a systematic control of denominators of critical values by generalized Kummer congruences. In order to organize this information we prove the existence...

The 2-adic eigencurve is proper.

Buzzard, Kevin, Calegari, Frank (2007)

Documenta Mathematica

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Anticyclotomic main conjectures.

Hida, Haruzo (2007)

Documenta Mathematica

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Companion forms and weight one forms.

Buzzard, Kevin, Taylor, Richard (1999)

Annals of Mathematics. Second Series

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On the characteristic power series of the U operator

Fernando Q. Gouvêa, Barry Mazur (1993)

Annales de l'institut Fourier

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We show that the coefficients of the characteristic power series of Atkin’s U operator acting on overconvergent $p$ -adic modular forms of weight $k$ vary $p$ -adically continuously as functions of $k$ . Are they in fact Iwasawa functions of $k$ ?

$p$ -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 $L (M, s) = \prod_{𝔭} L_{𝔭} (M, 𝒩 𝔭^{- s})$ is an Euler product $𝔭$ running through maximal ideals of the maximal order $𝒪_{F}$ of $F$ and $\begin{matrix} L_{𝔭} (M, X)^{- 1} & = (1 - α^{(1)} (𝔭) X) \cdot (1 - α^{(2)} (𝔭) X) \cdot ... \cdot (1 - α (d) (𝔭) X) \\ = 1 + A_{1} (𝔭) X + ... + A_{d} (𝔭) X^{d} \end{matrix}$ 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.

Displaying similar documents to “Admissible p -adic measures attached to triple products of elliptic cusp forms.”

Displaying similar documents to “Admissible $p$ -adic measures attached to triple products of elliptic cusp forms.”