论文标题
有限场上的Artin-Schreier曲线的质量公式
A Mass Formula For Artin--Schreier Curves Over Finite Fields
论文作者
论文摘要
我们研究了Artin的质量公式 - 在有限的字段$ k $的特征性$ p $上定义的属$ g $的曲线。对于奇数$ $ p $，对于小$ g $，我们确定$ k $ - 同构类别的属属属属属$ g $的曲线，这是由Artin-Schreier在自动形态组中的中心化订单加权的数量。这扩展了特征性$ p = 2 $的几位作者的早期结果。 关键字：Artin-Schreier曲线，有限场，自动形态，质量公式，模量空间，算术统计
We study a mass formula for Artin--Schreier curves of genus $g$ defined over a finite field $k$ of characteristic $p$. For an odd prime $p$ and for small $g$, we determine the number of $k$-isomorphism classes of Artin-Schreier curves of genus $g$, weighted by the order of the centralizer of the Artin-Schreier involution in the automorphism group. This extends earlier results by several authors in characteristic $p=2$. Keywords: Artin-Schreier curve, finite field, automorphism, Mass formula, moduli space, arithmetic statistics
