The archimedean Asai L-factor for GL_n(C) and the exterior-square L-factor for GL_m(F) are finite sums of Flicker and Jacquet-Shalika local zeta integrals, respectively.
On the Holomorphy of Exterior-Square L-functions
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abstract
In this paper, we show that the twisted partial exterior-square $L$-function has a meromorphic continuation to the whole complex plane with only two possible simple poles at $s=1$ and $s=0$. We do this by establishing the nonvanishing of the local zeta integrals defined by Jacquet and Shalika for any fixed $s_0$. The even case is treated in detail. The odd case is treated briefly, in which case, the $L$-function is shown to be entire.
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Finite-Sum Realization of Archimedean Asai and Exterior-Square $L$-Factors
The archimedean Asai L-factor for GL_n(C) and the exterior-square L-factor for GL_m(F) are finite sums of Flicker and Jacquet-Shalika local zeta integrals, respectively.