Non vanishing of products of twisted $\mathrm{GL}(3)$ $L$-functions
Number Theory
2021-12-17 v1
Abstract
In this paper, we prove that if the Fourier coefficients of a Hecke--Maa\ss\ cusp form are not too correlated with additive characters, then there exists infinitely many Dirichlet characters such that \begin{align*} L\left(\frac{1}{2},\pi\otimes\chi\right)L\left(\frac{1}{2},\chi\right)\neq 0. \end{align*} To prove this result, we compute the first twisted moment of these function averaged over a well chosen set of conductors.
Cite
@article{arxiv.2112.08927,
title = {Non vanishing of products of twisted $\mathrm{GL}(3)$ $L$-functions},
author = {Robin Frot},
journal= {arXiv preprint arXiv:2112.08927},
year = {2021}
}