Points algébriques de hauteur bornée sur la droite projective

Abstract

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.