The average least character nonresidue and further variations on a theme of Erdos

Greg Martin, Paul Pollack

For each nonprincipal Dirichlet character $\chi$, let $n_{\chi }$ be the least $n$ with $\chi (n)\notin \{0,1\}$. We show that as the average of $n_{\chi }$ over all nonprincipal characters $\chi$ modu…