Hauteur asymptotique des points de Heegner

Abstract

The asymptotic behaviour of the Neron-Tate height of Heegner points on a rational elliptic curve attached to an arithmetically normalized new cusp form f of weight 2, level N and trivial character is studied in this paper. By Gross-Zagier formula, this height is related to the special value at the critical point for the derivative of the Rankin-Selberg convolution of f with a certain weight one theta series attached to some ideal class of some imaginary quadratic field. Asymptotic formula for the first moments asociated to these Dirichlet series are proved and experimental results are carefully discussed.