论文标题
Hermitian曲线及其Weierstrass Semigroups上的理性点三元
Triples of rational points on the Hermitian curve and their Weierstrass semigroups
论文作者
论文摘要
在本文中，我们在$ \ mathbb {f} _ {q^2} $上研究了三个理性点的配置，并根据其Weierstrass Semigroups对它们进行分类。对于$ q> 3 $，我们表明该表格的不同半群的数量等于$ Q+1 $的正分数数量，并对所研究的每三个点进行明确描述Weierstrass Semigroup。为此，我们利用两点差异并得出适用于有限场上的任意曲线的标准。
In this paper, we study configurations of three rational points on the Hermitian curve over $\mathbb{F}_{q^2}$ and classify them according to their Weierstrass semigroups. For $q>3$, we show that the number of distinct semigroups of this form is equal to the number of positive divisors of $q+1$ and give an explicit description of the Weierstrass semigroup for each triple of points studied. To do so, we make use of two-point discrepancies and derive a criterion which applies to arbitrary curves over a finite field.
