Algebraic points of bounded height on the projective line

被引：4

作者：

Le Rudulier, Cecile ^{[1
]}

机构：

[1] Univ Rennes 1, IRMAR, F-35042 Rennes, France

来源：

JOURNAL DE THEORIE DES NOMBRES DE BORDEAUX | 2014年 / 26卷 / 03期

关键词：

INEQUALITY; THEOREM;

D O I：

10.5802/jtnb.888

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We consider an absolute adelic height on the set of algebraic points of the projective line P-1, associate to an ample line bundle. We give an asymptotic formula for the number of algebraic points of fixed degree and of height lower than B, when B tends to infinity. The case of the standard height on P-1 has been studied by Masser and Vaaler. We generalize this result for any adelic height using a geometric point of view and one of he known cases of the Batyrev-Manin conjecture.

引用

页码：789 / 812

页数：24

共 20 条

[1]

[Anonymous], 1997, ASPECTS MATH

[2]

Barroero F., 2013, ARXIC13050482

[3] THE NUMBER OF RATIONAL-POINTS OF BOUNDED HEIGHT OF ALGEBRAIC-VARIETIES [J].