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

Haruzo Hida

Displaying similar documents to “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

John Coates (1988-1989)

Séminaire Bourbaki

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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...

On the image of $Λ$ -adic Galois representations

Ami Fischman (2002)

Annales de l’institut Fourier

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We explore the question of how big the image of a Galois representation attached to a $Λ$ -adic modular form with no complex multiplication is and show that for a “generic” set of $Λ$ -adic modular forms (normalized, ordinary eigenforms with no complex multiplication), all have a large image.

On $p$ -adic analytic families of Galois representations

B. Mazur, A. Wiles (1986)

Compositio Mathematica

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Anti-cyclotomic Katz $p$ -adic $L$ -functions and congruence modules

H. Hida, J. Tilouine (1993)

Annales scientifiques de l'École Normale Supérieure

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On the p-adic Eichler-Shimura isomorphism for ...-adic cusp forms.

Masami Ohta (1995)

Journal für die reine und angewandte Mathematik

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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 “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”

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Displaying similar documents to “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

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