### Poles of triple tensor product L-fuctions involving monomial representations

Heilbronn Number Theory Seminar

18th November 2020, 11:00 am – 12:00 pm

Zoom (NOTE SPECIAL TIME),

Little is known about the order of poles of triple tensor product $L$-functions in higher rank. In this talk we will investigate 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 $\GL_{n_i}(\A_F)$ 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 talk give examples that can be used as a point of reference for Langlands' beyond endoscopy proposal.

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