论文标题
$ \ mathbb {p}^1 _ {\ mathbb {f} _q} $和一级密度
Lower Order Terms for Expected Value of Traces of Frobenius of a Family of Cyclic Covers of $\mathbb{P}^1_{\mathbb{F}_q}$ and One-Level Densities
论文作者
论文摘要
我们考虑$ \ mbox {tr}（θ_c^n）$的预期值，其中$ c $在$ r $ -r $ -cyclic封面上运行的$ \ mathbb {p}^1 _ {\ mathbb {f} _q} _我们获得了许多依赖$ r $的除数的低订单条款。我们使用这些结果来计算家庭的一级密度，并假设精致的一级密度结果。
We consider the expected value of $\mbox{Tr}(Θ_C^n)$ where $C$ runs over a thin family of $r$-cyclic covers of $\mathbb{P}^1_{\mathbb{F}_q}$ for any $r$. We obtain many lower order terms dependent on the divisors of $r$. We use these results to calculate the one-level density of the family and hypothesize a refined one-level density result.
