Shalika periods on 𝐺𝑈(2,2)

Furusawa, Masaaki; Morimoto, Kazuki

doi:10.1090/S0002-9939-2013-11690-4

Shalika periods on $\mathrm {GU}(2,2)$
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by Masaaki Furusawa and Kazuki Morimoto

Proc. Amer. Math. Soc. 141 (2013), 4125-4137

DOI: https://doi.org/10.1090/S0002-9939-2013-11690-4

Published electronically: August 15, 2013

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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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