Lehmer-type bounds and counting rational points of bounded heights on Abelian varieties

被引：0
|
作者：
Kumar, Narasimha [1 ]
Sahoo, Satyabrat [1 ]
机构：
[1] Indian Inst Technol Hyderabad, Dept Math, Sangareddy 502285, India
来源：
INTERNATIONAL JOURNAL OF NUMBER THEORY | 2024年 / 20卷 / 08期
关键词：
Abelian varieties; Neron-Tate heights; Lehmer-type bounds; Counting rational points; NERON-TATE HEIGHT; CANONICAL HEIGHT; NUMBER; VALUES;
D O I：
10.1142/S1793042124501045
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper, we study Lehmer-type bounds for the Neron-Tate height of (K) over tilde -points on abelian varieties A over number fields K. Then, we estimate the number of K-rational points on A with Neron-Tate height <= logB for B >> 0. This estimate involves a constant C, which is not explicit. However, for elliptic curves and the product of elliptic curves over K, we make the constant explicitly computable.
引用
收藏
页码：2125 / 2138
页数：14
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