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 $\chi (2)=1$.

16 pages, 2 figures. Submitted to International Journal of Number Theory