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

Abstract

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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 ∞ -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 ) × U ( n ) .

How to cite

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Eischen, 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 -

References

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