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.
Beuzart-Plessis, Archimedean theory and \( \)-factors for the Asai Rankin--Selberg integrals, in Relative Trace Formulas, Simons Symposia, Springer, Cham, 1--50, 2021
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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.