Extreme values of geodesic periods on arithmetic hyperbolic surfaces

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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https://hal.archives-ouvertes.fr/hal-02460213
Contributor : Bart Michels <>
Submitted on : Wednesday, January 29, 2020 - 10:10:35 PM
Last modification on : Friday, February 14, 2020 - 1:39:10 AM

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  • HAL Id : hal-02460213, version 1
  • ARXIV : 2002.05080

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Bart Michels. Extreme values of geodesic periods on arithmetic hyperbolic surfaces. 2020. ⟨hal-02460213v1⟩

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