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Shalika periods on $ \mathrm{GU}(2,2)$


Authors: Masaaki Furusawa and Kazuki Morimoto
Journal: Proc. Amer. Math. Soc. 141 (2013), 4125-4137
MSC (2010): Primary 11F67; Secondary 11F66
Published electronically: August 15, 2013
MathSciNet review: 3105856
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Abstract: In this paper we consider a certain Rankin-Selberg integral on a quasi-split similitude unitary group $ \mathrm {GU}\left (2,2\right )$, which is an analogue of Jacquet-Shalika's integral for the exterior square $ L$-function for $ \mathrm {GL}(2n)$ when $ n=2$. It indeed represents the twisted exterior square $ L$-function, and we study the relationship between the existence of a pole at $ s=1$ and the non-vanishing of a unitary analogue of the Shalika period.


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Masaaki Furusawa
Affiliation: Department of Mathematics, Graduate School of Science, Osaka City University, Sugimoto 3–3–138, Sumiyoshi-ku, Osaka 558-8585, Japan
Email: furusawa@sci.osaka-cu.ac.jp

Kazuki Morimoto
Affiliation: Department of Mathematics, Graduate School of Science, Osaka City University, Sugimoto 3–3–138, Sumiyoshi-ku, Osaka 558-8585, Japan
Email: kazukimorimo@gmail.com

DOI: https://doi.org/10.1090/S0002-9939-2013-11690-4
Received by editor(s): September 26, 2011
Received by editor(s) in revised form: February 7, 2012
Published electronically: August 15, 2013
Additional Notes: The research of the first author was supported in part by JSPS Grant-in-Aid for Scientific Research (C) 22540029
The research of the second author was supported in part by Grant-in-Aid for JSPS Fellows (23-6883) and JSPS Institutional Program for Young Researcher Overseas Visits project: Promoting international young researchers in mathematics and mathematical sciences led by OCAMI
Communicated by: Kathrin Bringmann
Article copyright: © Copyright 2013 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.