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Ellen E. Eischen
$p$-adic Differential Operators on Automorphic Forms on Unitary Groups
(Opérateurs différentiels $p$-adiques sur formes automorphes pour groupes unitaires)
Annales de l'institut Fourier, 62 no. 1 (2012), p. 177-243, doi: 10.5802/aif.2704
Article PDF | Reviews MR 2986270 | Zbl 1257.11054
Class. Math.: 14G35, 11G10, 11F03, 11F55, 11F60
Keywords: $p$-adic automorphic forms, differential operators, Maass operators

Résumé - Abstract

The goal of this paper is to study certain $p$-adic differential operators on automorphic forms on $U(n,n)$. These operators are a generalization to the higher-dimensional, vector-valued situation of the $p$-adic differential operators constructed for Hilbert modular forms by N. Katz. They are a generalization to the $p$-adic case of the $C^{\infty }$-differential operators first studied by H. Maass and later studied extensively by M. Harris and G. Shimura. The operators should be useful in the construction of certain $p$-adic $L$-functions attached to $p$-adic families of automorphic forms on the unitary groups $U(n)\times U(n)$.

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