Chaotic Aharonov-Bohm scattering on surfaces of constant negative curvature

A topological model of the Aharonov-Bohm scattering is presented, where the usual set-up is modelled by a genus-one Riemann surface with two cusps, i. e. leaks infinitely far away. This constant negative-curvature surface is u niformized by the Hecke congruence subgroup Gamma(0)(11) of the modular gro up. The fluxes through the holes are described by the even Dirichlet charac ter for Gamma(0)(11). The scattering matrix having only off-diagonal elemen ts (no reflection) is calculated. The fluctuating part of the off-diagonal entries shows a non-trivial dependence on the fluxes as well. The scatterin g resonances are related to the non-trivial zeros of a Dirichlet L-function . The chaotic nature of the scattering is related to the distribution of pr imes in arithmetical progressions.