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

Abstract

In this paper, we study Lehmer-type bounds for the Néron–Tate height of [Formula: see text]-points on abelian varieties A over number fields K. Then, we estimate the number of K-rational points on A with Néron–Tate height [Formula: see text] for [Formula: see text]. 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.