On the average number of rational points of bounded height on hyperelliptic curves

被引：1

作者：

Zinevicius, Albertas ^{[1
]}

机构：

[1] Vilnius Univ, Dept Math & Informat, Vilnius, Lithuania

来源：

BEITRAGE ZUR ALGEBRA UND GEOMETRIE-CONTRIBUTIONS TO ALGEBRA AND GEOMETRY | 2012年 / 53卷 / 01期

关键词：

Hyperelliptic curves; Rational points; Density; Height;

D O I：

10.1007/s13366-011-0050-x

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this note, an estimate for the average number of rational points of height at most H on genus g >= 2 curves is obtained. It gives the asymptotics of the average over curves of size up to N with error term O(N-1 H-2 + N-3/2 H-3). Lower asymptotic density of rational points of arbitrary height is described.

引用

页码：225 / 233

页数：9