Comportement asymptotique des hauteurs des points de Heegner

Details Comportement asymptotique des hauteurs des points de Heegner Comportement asymptotique des hauteurs des points de Heegner

2008-07-18

arxiv.org/abs/0807.2930v1

Mathematics

Number Theory

Scientific paper

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.

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