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.




     To study the Néron-Tate height of Heegner points on E.




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.





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