Nonvanishing of $L$--functions associated to fixed order characters over function fields

Chantal David, Alexandra Florea, Matilde Lalin

We show that a positive proportion of the values $L(1/2,{\chi }_c)$ are non-zero, where ${\chi }_c$ is the ${\ell }^{\text{th}}$ residue symbol for $\ell \ge 3$ over ${\mathbb{F}}_q[t]$, when aver…