Real zeros and size of Rankin-Selberg $L$-functions in the level aspect
G. Ricotta
Source: Duke Math. J. Volume 131, Number 2
(2006), 291-350.
Abstract
In this article, some asymptotic formulas are proved for the harmonic mollified second moment of a family of Rankin-Selberg $L$-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 $L$-functions in the level aspect. Moreover, infinitely many Rankin-Selberg $L$-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
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Permanent link to this document: http://projecteuclid.org/euclid.dmj/1137077886
Digital Object Identifier: doi:10.1215/S0012-7094-06-13124-1
Mathematical Reviews number (MathSciNet): MR2219243
Zentralblatt MATH identifier: 1122.11059
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