On an error term for the first moment of twisted $L$-functions

Xinyi He

Let $f$ be a Hecke-Maass cusp form for the full modular group and let $\chi$ be a primitive Dirichlet character modulo a prime $q$. Let $s_0={\sigma }_0+i{t}_0$ with $\frac{1}{2}\le {\sigma }_0<1$. We…