Equidistribution quantitative des points de petite hauteur sur la droite projective

We introduce a new class of adelic heights on the projective line. We estimate their essential minimum and prove a result of equidistribution (at every place) for points of small height with estimates on the speed of convergence. To each rational function R in one variable and defined over a number field K, is associated a normalized height on the algebraic closure of K. We show that these dynamically defined heights are adelic in our sense, and deduce from this equidistribution results for preimages of points under R at every place of K. Our approach follows that of Bilu, and relies on potential theory in the complex plane, as well as in the Berkovich space associated to the projective line over , for each prime p. Le premier auteur tient à remercier chaleureusement le project MECESUP UCN0202, ainsi que l'ACI ``Systèmes Dynamiques Polynomiaux' qui ont permis son séjour à l'Université Catholique d'Antofagasta. Le deuxième auteur est partiellement soutenu par le projet FONDECYT N 1040683. Enfin, nous remercions le rapporteur pour sa lecture détaillée de l'article.