Real zeros
and size of Rankin-Selberg
L-functions
Published in Duke
Mathematical Journal, Vol. 131, No. 2 (2006), 291--350.
Received 7
September 2004.
Revision received
20 February 2005.
In
this paper, some asymptotic formula is proved for the harmonic mollified second
moment of a family of Rankin-Selberg L-functions.
The
main contribution is a substancial improvement of the admissible length of the
mollifier which is done by solving a shifted convolution problem by a spectral
method on average.
Consequences :
·
new subconvexity bound,
· exponential decay of the analytic
rank,
· non-vanishing result around the real
axis.
You can find the files vg.mws,
cte.mws, ctemumubar.mws and inte.mws on the page of my thesis.
The previous texts are
not the published one. For they should not be quoted. Reprints of published
versions may be asked by e-mails.