Real zeros and size of Rankin-Selberg L-functions in the level aspect
Number Theory
2007-05-23 v1
Abstract
In this paper, some asymptotic formulas are proved for the harmonic mollified second moment of a family of Rankin-Selberg L-functions. One of the main new input is a substantial improvement of the admissible length of the mollifier which is done by solving a shifted convolution problem by a spectral method on average. A first consequence is a new subconvexity bound for Rankin-Selberg L-functions in the level aspect. Moreover, infinitely many Rankin-Selberg L-functions having at most eight non-trivial real zeros are produced and some new non-trivial estimates for the analytic rank of the family studied are obtained.
Keywords
Cite
@article{arxiv.math/0502470,
title = {Real zeros and size of Rankin-Selberg L-functions in the level aspect},
author = {Guillaume Ricotta},
journal= {arXiv preprint arXiv:math/0502470},
year = {2007}
}