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

被引：1

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

页码：2125 / 2138

页数：14

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