Moments of Traces of Frobenius of Higher Order Dirichlet $L$-functions over $\mathbb{F}_q[T]$

Patrick Meisner

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arXiv · 2108.07557

Moments of Traces of Frobenius of Higher Order Dirichlet $L$-functions over $\mathbb{F}_q[T]$

Patrick Meisner

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Abstract

We study the moments of $\mbox{Tr}(\Theta_\chi)$ 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 behave like the power sum moments of the group of unitary matrices multiplied by a weight function.

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Patrick Meisner. 2021-08-17. Moments of Traces of Frobenius of Higher Order Dirichlet $L$-functions over $\mathbb{F}_q[T]$. https://arxiv.org/abs/2108.07557

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