Mean square values of $L$-functions over subgroups for non primitive characters, Dedekind sums and bounds on relative class numbers

Stéphane R. Louboutin, Marc Munsch

An explicit formula for the mean value of $|L(1,\chi ){|}^2$ is known, where $\chi$ runs over all odd primitive Dirichlet characters of prime conductors $p$. Bounds on the relative…