## Duke Mathematical Journal

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

G. Ricotta

#### 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

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

#### 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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