2023 AN EXPLICIT FORMULA FOR THE SECOND MOMENT OF MAASS FORM SYMMETRIC SQUARE L-FUNCTIONS
Olga Balkanova, Dmitry Frolenkov
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Publ. Mat. 67(2): 611-660 (2023). DOI: 10.5565/PUBLMAT6722306

Abstract

We prove an explicit formula for the second moment of symmetric square L-functions associated to Maass forms for the full modular group. In particular, we show how to express the considered second moment in terms of dual second moments of symmetric square L-functions associated to Maass cusp forms of levels 4, 16, and 64.

Acknowledgements

We thank the referees for many helpful comments that helped us to improve the manuscript significantly.

Citation

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Olga Balkanova. Dmitry Frolenkov. "AN EXPLICIT FORMULA FOR THE SECOND MOMENT OF MAASS FORM SYMMETRIC SQUARE L-FUNCTIONS." Publ. Mat. 67 (2) 611 - 660, 2023. https://doi.org/10.5565/PUBLMAT6722306

Information

Received: 6 April 2021; Revised: 29 April 2022; Published: 2023
First available in Project Euclid: 29 June 2023

MathSciNet: MR4609014
zbMATH: 07720473
Digital Object Identifier: 10.5565/PUBLMAT6722306

Subjects:
Primary: 11F12 , 11F30 , 11M99

Keywords: Kloosterman sums , Kuznetsov trace formula , L-functions , regularization

Rights: Copyright © 2023 Universitat Autònoma de Barcelona, Departament de Matemàtiques

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Vol.67 • No. 2 • 2023
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