Lower Order Terms for Expected Value of Traces of Frobenius of a Family of Cyclic Covers of ${\mathbb{P}}_{{\mathbb{F}}_q}^1$ and One-Level Densities

Patrick Meisner

We consider the expected value of $\mbox{Tr}(Θ_C^n)$ where $C$ runs over a thin family of $r$-cyclic covers of ${\mathbb{P}}_{{\mathbb{F}}_q}^1$ for any $r$. We obtain many lower order…