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 Blasius-Deligne conjecture for the standard $L$-functions of symplectic type for $\textrm{GL}_{2n}$
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abstract
In this paper we give an unconditional proof of the Blasius-Deligne conjecture for the critical values of the $\textrm{GL}_{2n}$-standard $L$-functions of symplectic type with $n\geq 1$ and complete the project started in [JST19].
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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.