Extreme values of geodesic periods on arithmetic hyperbolic surfaces
Number Theory
2020-12-23 v2 Spectral Theory
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.
Cite
@article{arxiv.2002.05080,
title = {Extreme values of geodesic periods on arithmetic hyperbolic surfaces},
author = {Bart Michels},
journal= {arXiv preprint arXiv:2002.05080},
year = {2020}
}