Exceptional poles of archimedean Rankin-Selberg L-functions for irreducible generic representations of GL(n,R)

Abstract

For irreducible generic representations ${\pi }_1$ and ${\pi }_2$ of ${\mathrm{GL}}_n(\mathbb{R})$, we prove that the notions of exceptional pole of type $1$ and type $2$ coincide at every level. When both representations are in general position, we use this identification to express the Rankin--Selberg $L$-function $L(s,{\pi }_1\times {\pi }_2)$ in terms of the exceptional $L$-factors attached to the irreducible constituents of their derivatives.

36 pages, main result extended to all irreducible generic representations