Moments of traces of Frobenius of higher order Dirichlet $L$-functions over $\mathbb F_q[T]$
Volume 208 / 2023
Acta Arithmetica 208 (2023), 127-159
MSC: Primary 11M26; Secondary 11M38, 11M50.
DOI: 10.4064/aa220705-24-1
Published online: 11 April 2023
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 like the power sum moments of the group of unitary matrices multiplied by a weight function.
