On congruence modules associated to $\Lambda $-adic forms

Fred Diamond

Displaying similar documents to “On congruence modules associated to $Λ$ -adic forms”

Congruence modules related to Eisenstein series

Masami Ohta (2003)

Annales scientifiques de l'École Normale Supérieure

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Iwasawa modules attached to congruences of cusp forms

Haruzo Hida (1986)

Annales scientifiques de l'École Normale Supérieure

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Control theorems of $p$ -nearly ordinary cohomology groups for $SL (n)$

Haruzo Hida (1995)

Bulletin de la Société Mathématique de France

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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...

$p$ -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...

p-adic deformations of cohomology classes of subgroups of GL (N,Z).

Avner Ash, Glenn Stevens (1997)

Collectanea Mathematica

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Displaying similar documents to “On congruence modules associated to Λ -adic forms”

Congruence modules related to Eisenstein series

Iwasawa modules attached to congruences of cusp forms

Control theorems of p -nearly ordinary cohomology groups for SL ( n )

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

p -adic ordinary Hecke algebras for GL ( 2 )

p-adic deformations of cohomology classes of subgroups of GL (N,Z).

Displaying similar documents to “On congruence modules associated to $Λ$ -adic forms”

Control theorems of $p$ -nearly ordinary cohomology groups for $SL (n)$

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

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