Constructions of p-adic L-functions and admissible measures for Hermitian modular forms - Archive ouverte HAL Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2018

Constructions of p-adic L-functions and admissible measures for Hermitian modular forms

Constructions de fonctions L-functions p-adiques et mesures admissibles de formes modulaires hermitiehhes

Alexei Pantchichkine
  • Fonction : Auteur
  • PersonId : 866010

Résumé

For a prime p and a positive integer n, the standard zeta function L_F (s) is considered, attached to an Hermitian modular form F =\sum_ H A(H)q^H on the Hermitian upper half plane H_n of degree n, where H runs through semi-integral positive definite Hermitian matrices of degree n, i.e. H \in \Lambda_n(O) over the integers O of an imaginary quadratic field K, where q^H = exp(2 iTr(HZ)). Analytic p- adic continuation of their zeta functions constructed by A.Bouganis in the ordinary case (in [Bou16] is presently extended to the admissible case via growing p-adic measures. Previously this problem was solved for the Siegel modular forms, [CourPa], [BS00]. Present main result is stated in terms of the Hodge polygon P_H(t) : [0; d] ! R and the Newton polygon P_N(t) = P_{N;p}(t) : [0; d] -> R of the zeta function L_F (s) of degree d = 4n. Main theorem gives a p-adic analytic interpolation of the L values in the form of certain integrals with respect to Mazur-type measures.
Fichier principal
Vignette du fichier
2018-article-Sarajevo.pdf (2.88 Mo) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-01875160 , version 1 (17-09-2018)

Identifiants

  • HAL Id : hal-01875160 , version 1

Citer

Alexei Pantchichkine. Constructions of p-adic L-functions and admissible measures for Hermitian modular forms. 2018. ⟨hal-01875160⟩

Collections

UGA CNRS FOURIER
75 Consultations
36 Téléchargements

Partager

Gmail Facebook X LinkedIn More