Comportement asymptotique des hauteurs des points de Heegner
Number Theory
2008-07-21 v1 Algebraic Geometry
Abstract
The leading order term for the average, over quadratic discriminants satisfying the so-called Heegner condition, of the Neron-Tate height of Heegner points on a rational elliptic curve E has been determined in [12]. In addition, the second order term has been conjectured. In this paper, we prove that this conjectured second order term is the right one; this yields a power saving in the remainder term. Cancellations of Fourier coefficients of GL(2)-cusp forms in arithmetic progressions lie in the core of the proof.
Keywords
Cite
@article{arxiv.0807.2930,
title = {Comportement asymptotique des hauteurs des points de Heegner},
author = {Guillaume Ricotta and Nicolas Templier},
journal= {arXiv preprint arXiv:0807.2930},
year = {2008}
}