# 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} }

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.

## One Citation

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We prove a new omega result for toric periods of Hecke-Maass forms on compact locally symmetric spaces associated to forms of PGL3. This is motivated by conjectures on the maximal growth of…

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