# $p$-adic Differential Operators on Automorphic Forms on Unitary Groups

Ellen E. Eischen^{[1]}

- [1] Mathematics Department Northwestern University 2033 Sheridan road Evanston, IL 60208 USA

Annales de l’institut Fourier (2012)

- Volume: 62, Issue: 1, page 177-243
- ISSN: 0373-0956

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topEischen, Ellen E.. "$p$-adic Differential Operators on Automorphic Forms on Unitary Groups." Annales de l’institut Fourier 62.1 (2012): 177-243. <http://eudml.org/doc/251035>.

@article{Eischen2012,

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 $U(n)\times U(n)$.},

affiliation = {Mathematics Department Northwestern University 2033 Sheridan road Evanston, IL 60208 USA},

author = {Eischen, Ellen E.},

journal = {Annales de l’institut Fourier},

keywords = {$p$-adic automorphic forms; differential operators; Maass operators; -adic automorphic forms},

language = {eng},

number = {1},

pages = {177-243},

publisher = {Association des Annales de l’institut Fourier},

title = {$p$-adic Differential Operators on Automorphic Forms on Unitary Groups},

url = {http://eudml.org/doc/251035},

volume = {62},

year = {2012},

}

TY - JOUR

AU - Eischen, Ellen E.

TI - $p$-adic Differential Operators on Automorphic Forms on Unitary Groups

JO - Annales de l’institut Fourier

PY - 2012

PB - Association des Annales de l’institut Fourier

VL - 62

IS - 1

SP - 177

EP - 243

AB - 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 $U(n)\times U(n)$.

LA - eng

KW - $p$-adic automorphic forms; differential operators; Maass operators; -adic automorphic forms

UR - http://eudml.org/doc/251035

ER -

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