Extreme values of geodesic periods on arithmetic hyperbolic surfaces

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.