Moments of traces of Frobenius of higher order Dirichlet $L$-functions over $\mathbb F_q[T

Abstract

We study the moments of ${\rm Tr}(\Theta _\chi)$ as $\chi $ runs over Dirichlet characters defined over $\mathbb F_q[T]$ of fixed order $r$. In particular, we show that after an appropriate normalization, the $q$-limit of the power sum moments behaves lik