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

Abstract

In this article, we study Lehmer-type bounds for the Néron-Tate height of $\bar{K}$-points on abelian varieties $A$ over number fields $K$. Then, we estimate the number of $K$-rational points on $A$ with Néron-Tate height $\le \log B$ for $B\gg 0$. 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.

To appear in the International Journal of Number Theory