$p$-adic interpolation of special values of Hecke L-functions

Pierre Colmez; Leila Schneps

Displaying similar documents to “ $p$ -adic interpolation of special values of Hecke L-functions”

A new construction of $p$ -adic $L$ -functions attached to certain elliptic curves with complex multiplication

John L. Boxall (1986)

Annales de l'institut Fourier

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In this paper we apply the results of our previous article on the $p$ -adic interpolation of logarithmic derivatives of formal groups to the construction of $p$ -adic $L$ -functions attached to certain elliptic curves with complex multiplication. Our results are primarily concerned with curves with supersingular reduction.

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...

On $p$ -adic $L$ -functions

John Coates (1988-1989)

Séminaire Bourbaki

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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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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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A Kummer criterion for imaginary quadratic fields

Rodney I. Yager (1982)

Compositio Mathematica

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

Shai Haran (1987)

Compositio Mathematica

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Displaying similar documents to “ p -adic interpolation of special values of Hecke L-functions”

A new construction of p -adic L -functions attached to certain elliptic curves with complex multiplication

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

On p -adic L -functions

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

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

A Kummer criterion for imaginary quadratic fields

p -adic L -functions for modular forms

Displaying similar documents to “ $p$ -adic interpolation of special values of Hecke L-functions”

A new construction of $p$ -adic $L$ -functions attached to certain elliptic curves with complex multiplication

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

On $p$ -adic $L$ -functions

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

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

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