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Non vanishing of products of twisted $\mathrm{GL}(3)$ $L$-functions by Frot, Robin is a scholarly article available to read on EtoBox.

What is Non vanishing of products of twisted $\mathrm{GL}(3)$ $L$-functions about?

In this paper, we prove that if the Fourier coefficients of a $\mathrm{SL}(3,\mathbb{Z})$ Hecke--Maa\ss\ cusp form $\pi$ 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 $L$ function averaged over a well chosen set of conductors.

Author

Frot, Robin

Published

2021

Language

EN