# EXTREME VALUES OF GEODESIC PERIODS ON ARITHMETIC HYPERBOLIC SURFACES

@article{Michels2020EXTREMEVO,
title={EXTREME VALUES OF GEODESIC PERIODS ON ARITHMETIC HYPERBOLIC SURFACES},
author={Bart Michels},
journal={Journal of the Institute of Mathematics of Jussieu},
year={2020},
volume={21},
pages={1507 - 1542}
}
• Bart Michels
• Published 12 February 2020
• Mathematics
• Journal of the Institute of Mathematics of Jussieu
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.
1 Citations

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