Abstract
In this article, some asymptotic formulas are proved for the harmonic mollified second moment of a family of Rankin-Selberg -functions. One of the main new inputs 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 -functions in the level aspect. Moreover, infinitely many Rankin-Selberg -functions having at most eight nontrivial real zeros are produced, and some new nontrivial estimates for the analytic rank of the family studied are obtained
Citation
G. Ricotta. "Real zeros and size of Rankin-Selberg -functions in the level aspect." Duke Math. J. 131 (2) 291 - 350, 01 February 2006. https://doi.org/10.1215/S0012-7094-06-13124-1
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