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EXTREME VALUES OF GEODESIC PERIODS ON ARITHMETIC HYPERBOLIC SURFACES

Published online by Cambridge University Press:  22 December 2020

Bart Michels
Affiliation:
Université Sorbonne Paris Nord, LAGA, CNRS, UMR 7539, F-93430, Villetaneuse, France (michels@math.univ-paris13.fr)
Corresponding

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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Research Article
Copyright
© The Author(s), 2020. Published by Cambridge University Press

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