On a number of rational points on a plane curve of low degree
On a number of rational points on a plane curve of low degree
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低次平面曲线上的多个有理点
DOI：
10.1016/j.disc.2017.01.017
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发表时间：
2017
影响因子：
0.8
通讯作者：
and Namyong Lee
中科院分区：
文献类型：
--
作者：
Eun Ju Cheon;Masaaki Homma;Seon Jeong Kim;and Namyong Lee
摘要 Homma 和 Kim (2010) 发现了 F q 上 d 次平面曲线上有理点数量的上限。 Homma 和 Kim (2010) 中给出了一些达到界限的例子，其次数为 q+ 2、q+ 1、q、q− 1、q− 1（当 q 是正方形时）和 2。在本文中，我们考虑了 q≤ 7 的低次数曲线的实际上限。我们还给出了每个 d 和 q 达到尖锐界限的曲线的明确示例。
Abstract In Homma and Kim (2010), an upper bound of the number of rational points on a plane curve of degree d over F q is found. Some examples attaining the bound are given in Homma and Kim (2010), whose degrees are q+ 2, q+ 1, q, q− 1, q− 1 (when q is a square), and 2. In this paper, we consider an actual upper bound on such numbers for curves of low degree for q≤ 7. Also we give explicit examples of curves attaining the sharp bound for each d and q.