Real zeros and size of Rankin-Selberg






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. RSzerospdf.pdf


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.