One-level density of zeros of Dirichlet $L$-functions over function fields

Hua Lin

We compute the one-level density of zeros of order $\ell$ Dirichlet $L$-functions over function fields ${\mathbb{F}}_q[t]$ for $\ell =3,4$ in the Kummer setting ($q\equiv 1(\mathrm{mod}\ell )$…