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EXTREME VALUES OF GEODESIC PERIODS ON ARITHMETIC HYPERBOLIC SURFACES

Part of: Discontinuous groups and automorphic forms

Published online by Cambridge University Press:  22 December 2020

Bart Michels Open the ORCID record for Bart Michels [Opens in a new window]
Bart Michels*
Affiliation:
Université Sorbonne Paris Nord, LAGA, CNRS, UMR 7539, F-93430, Villetaneuse, France ([email protected])
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Abstract

Given a closed geodesic on a compact arithmetic hyperbolic surface, we show the existence of a sequence of Laplacian eigenfunctions whose integrals along the geodesic exhibit nontrivial growth. Via Waldspurger’s formula we deduce a lower bound for central values of Rankin-Selberg L-functions of Maass forms times theta series associated to real quadratic fields.

Keywords

L-functionsMaass formsclosed geodesicsamplification method

MSC classification

Primary: 11F03: Modular and automorphic functions
Secondary: 11F72: Spectral theory; Selberg trace formula
Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 21 , Issue 5 , September 2022 , pp. 1507 - 1542
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Copyright
© The Author(s), 2020. Published by Cambridge University Press

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