2008/07/18 by Guillaume Ricotta, Ricotta, Guillaume, Nicolas Templier +1 · 1 citation
Mathematics · #11G50 #11M41 #Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT) #math.AG #math.NT #msc:11G50 #msc:11M41
paper · pdf · doi:10.48550/arxiv.0807.2930
arxiv created 2008/07/18 · arxiv updated 2009/12/01
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.