Extreme values of geodesic periods on arithmetic hyperbolic surfaces

Valeurs extrêmes des périodes géodésiques sur les surfaces hyperboliques arithmétiques

Bart Michels (1)

1 LAGA - Laboratoire Analyse, Géométrie et Applications

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.

Domaines: Théorie des nombres [math.NT]; Théorie spectrale [math.SP]

Bart Michels. Extreme values of geodesic periods on arithmetic hyperbolic surfaces. 2020. ⟨hal-02460213v1⟩