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 Rankin--Selberg L-functions of Maass forms times theta series associated to real quadratic fields.

References in corpus (4)

• Large GCD sums and extreme values of the Riemann zeta function
• Quantum ergodicity for restrictions to hypersurfaces
• Lower bounds for Maass forms on semisimple groups
• Equidistribution of Eisenstein series on geodesic segments