A $p$-adic measure attached to the zeta functions associated with two elliptic modular forms. II

Haruzo Hida

Displaying similar documents to “A $p$ -adic measure attached to the zeta functions associated with two elliptic modular forms. II”

On $p$ -adic $L$ -functions of $G L (2) \times G L (2)$ 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 $G L (2) \times G L (2)$ 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 for modular forms

Shai Haran (1987)

Compositio Mathematica

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$p$ -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...

On the local behaviour of ordinary $Λ$ -adic representations

Eknath Ghate, Vinayak Vatsal (2004)

Annales de l'Institut Fourier

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Let $f$ be a primitive cusp form of weight at least 2, and let $ρ_{f}$ be the $p$ -adic Galois representation attached to $f$ . If $f$ is $p$ -ordinary, then it is known that the restriction of $ρ_{f}$ to a decomposition group at $p$ is “upper triangular”. If in addition $f$ has CM, then this representation is even “diagonal”. In this paper we provide evidence for the converse. More precisely, we show that the local Galois representation is not diagonal, for all except possibly finitely many of the arithmetic members...

On the search of genuine $p$ -adic modular $L$ -functions for $G L (n)$ . With a correction to: On $p$ -adic $L$ -functions of $G L (2) \times G L (2)$ over totally real fields

Haruzo Hida (1996)

Mémoires de la Société Mathématique de France

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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....

Displaying similar documents to “A p -adic measure attached to the zeta functions associated with two elliptic modular forms. II”

On p -adic L -functions of G L ( 2 ) × G L ( 2 ) over totally real fields

p -adic L -functions for modular forms

p -adic ordinary Hecke algebras for GL ( 2 )

On the local behaviour of ordinary Λ -adic representations

On the search of genuine p -adic modular L -functions for G L ( n ) . With a correction to: On p -adic L -functions of G L ( 2 ) × G L ( 2 ) over totally real fields

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

Displaying similar documents to “A $p$ -adic measure attached to the zeta functions associated with two elliptic modular forms. II”

On $p$ -adic $L$ -functions of $G L (2) \times G L (2)$ over totally real fields

$p$ -adic $L$ -functions for modular forms

$p$ -adic ordinary Hecke algebras for $GL (2)$

On the local behaviour of ordinary $Λ$ -adic representations

On the search of genuine $p$ -adic modular $L$ -functions for $G L (n)$ . With a correction to: On $p$ -adic $L$ -functions of $G L (2) \times G L (2)$ over totally real fields

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