Duke Mathematical Journal

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

G. Ricotta

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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

Article information

Source
Duke Math. J., Volume 131, Number 2 (2006), 291-350.

Dates
First available in Project Euclid: 12 January 2006

Permanent link to this document
https://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

Subjects
Primary: 11M41: Other Dirichlet series and zeta functions {For local and global ground fields, see 11R42, 11R52, 11S40, 11S45; for algebro-geometric methods, see 14G10; see also 11E45, 11F66, 11F70, 11F72}

Citation

Ricotta, G. Real zeros and size of Rankin-Selberg $L$ -functions in the level aspect. Duke Math. J. 131 (2006), no. 2, 291--350. doi:10.1215/S0012-7094-06-13124-1. https://projecteuclid.org/euclid.dmj/1137077886


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