Poles of triple product $L$-functions involving monomial representations

Heekyoung Hahn

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arXiv · 1912.04256

Poles of triple product $L$-functions involving monomial representations

Heekyoung Hahn

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Abstract

In this paper, we study the order of the pole of the triple tensor product $L$-functions $L(s,\pi_1\times\pi_2\times\pi_3,\otimes^3)$ for cuspidal automorphic representations $\pi_i$ of $\mathrm{GL}_{n_i}(\mathbb{A}_F)$ in the setting where one of the $\pi_i$ is a monomial representation. In the view of Brauer theory, this is a natural setting to consider. The results provided in this paper give crucial examples that can be used as a point of reference for Langlands' beyond endoscopy proposal.

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Heekyoung Hahn. 2019-12-09. Poles of triple product $L$-functions involving monomial representations. https://arxiv.org/abs/1912.04256

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