Comportement asymptotique des hauteurs des points de Heegner
(Asymptotic behaviour for
heights of Heegner points)
Submitted
on July 18, 2008.
Accepted
for publication on February 20, 2009.
Published in Journal de théorie des nombres de Bordeaux
21, no. 3, 741—753 (2009).
E
is a fixed elliptic curve over the rational numbers.
Purpose:
To study the Néron-Tate
height of Heegner points on E.
Result:
We
get an asymptotic formula for the Néron-Tate height
of Heegner points on E on average over a subset of discriminants. The first and second order terms are
obtained and a power saving in the remainder term is proved. Cancellations of
Fourier coefficients of automorphic forms lie in the
core of the proof.
The previous texts are
not the published one. For they should not be quoted.
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