# Zéros réels et taille des fonctions L de Rankin-Selberg par rapport au niveau

Abstract : This thesis establishes some strong asymptotic formulae for the harmonic mollified second moment of a family of Rankin-Selberg $L$-functions. The main contribution is a substancial 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 sharp subconvexity bound for Rankin-Selberg L-functions in the level aspect which has many already known arithmetic applications. Moreover, infinitely many Rankin-Selberg L-functions having at most eight non-trivial real zeros are produced and some new non-trivial estimates of the analytic rank of the family studied are obtained.
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Theses
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https://tel.archives-ouvertes.fr/tel-00006428
Contributor : Guillaume Ricotta <>
Submitted on : Thursday, July 8, 2004 - 4:58:46 PM
Last modification on : Wednesday, February 12, 2020 - 11:40:06 AM
Long-term archiving on: : Wednesday, September 12, 2012 - 4:35:32 PM

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• HAL Id : tel-00006428, version 1

### Citation

Guillaume Ricotta. Zéros réels et taille des fonctions L de Rankin-Selberg par rapport au niveau. Mathématiques [math]. Université Montpellier II - Sciences et Techniques du Languedoc, 2004. Français. ⟨tel-00006428⟩

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