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 RankinSelberg Lfunctions of Maass forms times theta series associated to real quadratic fields.
 Publication:

arXiv eprints
 Pub Date:
 February 2020
 arXiv:
 arXiv:2002.05080
 Bibcode:
 2020arXiv200205080M
 Keywords:

 Mathematics  Number Theory;
 Mathematics  Spectral Theory
 EPrint:
 doi:10.1017/S147474802000064X