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

Heekyoung Hahn

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

Number Theory 2019-12-10 v1

Authors: Heekyoung Hahn

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.

Keywords

triple product l-functions monomial representations cuspidal automorphic representations pole order brauer theory langlands beyond endoscopy

Cite

@article{arxiv.1912.04256,
  title  = {Poles of triple product $L$-functions involving monomial representations},
  author = {Heekyoung Hahn},
  journal= {arXiv preprint arXiv:1912.04256},
  year   = {2019}
}

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

Abstract

Keywords

Cite

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