Exceptional poles of archimedean Asai $L$-functions

Abstract

Let $\pi$ be an irreducible generic representation of ${\mathrm{GL}}_n(\mathbb{C})$. We classify the exceptional poles of the associated Asai $L$-function $L(s,\pi ,\mathrm{As})$ and give a representation-theoretic characterization of them. When $\pi$ is in general position, we further express $L(s,\pi ,\mathrm{As})$ in terms of the exceptional $L$-factors attached to the irreducible constituents occurring in the derivatives of $\pi$.

arXiv comment20 pages