Real zeros and size of Rankin-Selberg L-functions in the level aspect

2005/02/23 by Guillaume Ricotta, Ricotta, Guillaume
Mathematics · #11M41 #FOS: Mathematics #Number Theory (math.NT) #math.NT #msc:11M41

paper · pdf · doi:10.48550/arxiv.math/0502470

arxiv created 2005/02/23 · arxiv updated 2009/12/01

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.

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