Explicit upper bound for $\left|L(1, \chi)\right|$ when $\chi(2)=1$ and $\chi$ is even

Abstract

Let $\chi$ be a primitive Dirichlet character of conductor $q$ and let us denote by $L(z, \chi)$ the associated $L$-series. In this paper, we provide an explicit upper bound for $\left|L(1, \chi)\right|$ when $\chi$ is a primitive even Dirichlet character with $\chi(2)=1$.