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A MEAN VALUE RESULT FOR A PRODUCT OF GL(2) AND GL(3) $L$-FUNCTIONS

Part of: Discontinuous groups and automorphic forms Asymptotic theory

Published online by Cambridge University Press:  17 April 2019

Olga Balkanova ,
Gautami Bhowmik ,
Dmitry Frolenkov  and
Nicole Raulf
Olga Balkanova
Affiliation:
Department of Mathematics and Statistics, University of Turku, Turku 20014, Finland Department of Mathematical Sciences, Chalmers University of Technology and University of Gothenburg, Chalmers tvärgata 3, 412 96 Gothenburg, Sweden email [email protected]
Gautami Bhowmik
Affiliation:
Laboratoire Painlevé LABEX-CEMPI, Université Lille, 59655 Villeneuve d’Ascq Cedex, France email [email protected]
Dmitry Frolenkov
Affiliation:
National Research University Higher School of Economics, Moscow, Russia Steklov Mathematical Institute of Russian Academy of Sciences, 8 Gubkina st., Moscow 119991, Russia email [email protected]
Nicole Raulf
Affiliation:
Laboratoire Painlevé LABEX-CEMPI, Université Lille, 59655 Villeneuve d’Ascq Cedex, France email [email protected]
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Abstract

In this paper various analytic techniques are combined in order to study the average of a product of a Hecke $L$-function and a symmetric square $L$-function at the central point in the weight aspect. The evaluation of the second main term relies on the theory of Maaß forms of half-integral weight and the Rankin–Selberg method. The error terms are bounded using the Liouville–Green approximation.

MSC classification

Primary: 11F12: Automorphic forms, one variable
Secondary: 33C05: Classical hypergeometric functions, $_2F_1$ 34E05: Asymptotic expansions 34E20: Singular perturbations, turning point theory, WKB methods
Type
Research Article
Information
Mathematika , Volume 65 , Issue 3 , 2019 , pp. 743 - 762
Copyright
Copyright © University College London 2019 

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Footnotes

The research of Olga Balkanova is supported by Academy of Finland project no. 293876. Gautami Bhowmik acknowledges support from the Labex CEMPI. The research of Dmitry Frolenkov is supported by the Foundation for the Advancement of Theoretical Physics and Mathematics BASIS. Nicole Raulf acknowledges support from the Labex CEMPI.

References

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