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# Mathematics > Number Theory

# Title: Extreme values of geodesic periods on arithmetic hyperbolic surfaces

(Submitted on 12 Feb 2020 (v1), last revised 13 Feb 2020 (this version, v2))

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.

## Submission history

From: Bart Michels [view email]**[v1]**Wed, 12 Feb 2020 16:35:43 GMT (32kb)

**[v2]**Thu, 13 Feb 2020 10:53:36 GMT (32kb)

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