有限域上具有给定点数的椭圆曲线
数论
2019-02-20 v4
摘要
给定一条椭圆曲线和一个正整数，我们考虑计数素数的个数的问题，使得模的约化在上恰好有个点。平均而言（在一族椭圆曲线上），我们给出的界显著优于由Hasse界平凡得到的界。在包括关于算术级数中素数短区间分布的一个猜想在内的若干附加假设下，我们得到了平均值的渐近公式。
引用
@article{arxiv.1108.3539,
title = {Elliptic curves with a given number of points over finite fields},
author = {Chantal David and Ethan Smith},
journal= {arXiv preprint arXiv:1108.3539},
year = {2019}
}
备注
A mistake was discovered in the derivation of the product formula for K(N). The included corrigendum corrects this mistake. All page numbers in the corrigendum refer to the journal version of the manuscript