Ricotta, Templier: Comportement asympotique des hauteurs des points de Heegner

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Guillaume Ricotta; Nicolas Templier
Comportement asympotique des hauteurs des points de Heegner
Journal de théorie des nombres de Bordeaux, 21 no. 3 (2009), p. 743-755
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Class. Math.: 11G50, 11M41

Résumé - Abstract

Asymptotic behaviour for the averaged height of Heegner points

The leading order term for the average, over quadratic discriminants satisfying the so-called Heegner condition, of the Néron-Tate height of Heegner points on a rational elliptic curve $E$ has been determined in [13]. 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 $G L_{2}$ -cusp forms in arithmetic progressions lie in the core of the proof.

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