Simultaneous nonvanishing of Dirichlet $L$-functions and twists of Hecke-Maass L-functions

Abstract

We prove that given a Hecke-Maass form $f$ for $\text{SL}(2,\mathbb{Z})$ and a sufficiently large prime $q$, there exists a primitive Dirichlet character $\chi$ of conductor $q$ such that the $L$-values $L(\frac{1}{2},f\otimes \chi )$ and $L(\frac{1}{2},\chi )$ do not vanish. We expect the same method to work for any large integer $q$.

Cited by in corpus (2)

• A note on simultaneous nonvanishing of Dirichlet $L$-functions and twists of Hecke-Maass $L$-functions
• Simultaneous non-vanishing for Dirichlet L-functions