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arXiv · 2002.05080

Extreme values of geodesic periods on arithmetic hyperbolic surfaces

Bart Michels
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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.

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Bart Michels. 2020-02-12. Extreme values of geodesic periods on arithmetic hyperbolic surfaces. https://doi.org/10.1017/s147474802000064x

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