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

Alexei A. Panchishkin

Displaying similar documents to “Motives over totally real fields and $p$ -adic $L$ -functions”

$p$ -adic $L$ -functions of Hilbert modular forms

Andrzej Dabrowski (1994)

Annales de l'institut Fourier

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We construct $p$ -adic $L$ -functions (in general case unbounded) attached to “motivic" primitive Hilbert cusp forms as a non-archimedean Mellin transform of the corresponding admissible measure. In order to prove the growth conditions of the appropriate complex-valued distributions we represent them as Rankin type representation and use Atkin–Lehner theory and explicit form of Fourier coefficients of Eisenstein series.

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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On $p$ -adic $L$ -functions

John Coates (1988-1989)

Séminaire Bourbaki

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

Shai Haran (1987)

Compositio Mathematica

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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...

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 $f = \sum_{n = 1}^{\infty} a (n) q^{n}$ and $g = \sum_{n = 1}^{\infty} b (n) q^{n}$ 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 $ℓ$ , respectively. Define the Rankin product of $f$ and $g$ by $𝒟_{N} (s, f, g) = (\sum_{n = 1}^{\infty} ψ ξ (n) n^{k + ℓ - 2 s - 2}) (\sum_{n = 1}^{\infty} a (n) b (n) n^{- s}) .$ Supposing $f$ and $g$ to be ordinary at a prime $p \geq 5$ , we shall construct a $p$ -adically analytic $L$ -function of three variables which interpolate the values $\frac{𝒟_{N} (ℓ + m, f, g)}{π^{ℓ + 2 m + 1} < f, f >}$ for integers $m$ with $0 \leq m < k - 1,$ by regarding all the ingredients $m$ , $f$ and $g$ as variables. Here $⟨ f, f ⟩$ is the Petersson...

Displaying similar documents to “Motives over totally real fields and p -adic L -functions”

p -adic L -functions of Hilbert modular forms

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

On p -adic L -functions

p -adic L -functions for modular forms

On the local behaviour of ordinary Λ -adic representations

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

Displaying similar documents to “Motives over totally real fields and $p$ -adic $L$ -functions”

$p$ -adic $L$ -functions of Hilbert modular forms

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

On $p$ -adic $L$ -functions

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

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

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