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2008 Commutation relations of Hecke operators for Arakawa lifting
Atsushi Murase, Hiro-aki Narita
Tohoku Math. J. (2) 60(2): 227-251 (2008). DOI: 10.2748/tmj/1215442873


T. Arakawa, in his unpublished note, constructed and studied a theta lifting from elliptic cusp forms to automorphic forms on the quaternion unitary group of signature $(1, q)$. The second named author proved that such a lifting provides bounded (or cuspidal) automorphic forms generating quaternionic discrete series. In this paper, restricting ourselves to the case of $q=1$, we reformulate Arakawa's theta lifting as a theta correspondence in the adelic setting and determine a commutation relation of Hecke operators satisfied by the lifting. As an application, we show that the theta lift of an elliptic Hecke eigenform is also a Hecke eigenform on the quaternion unitary group. We furthermore study the spinor $L$-function attached to the theta lift.


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Atsushi Murase. Hiro-aki Narita. "Commutation relations of Hecke operators for Arakawa lifting." Tohoku Math. J. (2) 60 (2) 227 - 251, 2008.


Published: 2008
First available in Project Euclid: 7 July 2008

zbMATH: 1214.11062
MathSciNet: MR2428862
Digital Object Identifier: 10.2748/tmj/1215442873

Primary: 11F55

Rights: Copyright © 2008 Tohoku University


Vol.60 • No. 2 • 2008
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