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arXiv · 2604.22259

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

Yeongseong Jo·Santosh Nadimpalli·Akash Yadav
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Abstract

We prove that for any pair of irreducible principal series representations $(\pi_1,\pi_2)$ of $\operatorname{GL}_n(\mathbb{R})$ in general position, the notions of exceptional pole of type 1 and type 2 coincide. Using this identification, we 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 the derivatives of $\pi_1$ and $\pi_2$.

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Yeongseong Jo, Santosh Nadimpalli, Akash Yadav. 2026-04-24. Exceptional poles of archimedean Rankin-Selberg L-functions for principal series representations of GL(n,R). https://arxiv.org/abs/2604.22259

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