A note on simultaneous nonvanishing of Dirichlet $L$-functions and twists of Hecke-Maass $L$-functions

Qingfeng Sun

In this note, we prove that given a Hecke-Maass cusp form $f$ for $S{L}_2(\mathbb{Z})$ and a sufficiently large integer $q=q_1{q}_2$ with $q_j\asymp \sqrt{q}$ being prime numbers for $…