For any Fuchsian group of the first kind and any even weight greater than 2, we prove that the relative Poincaré series associated to closed geodesics generate the space of cusp forms of the given weight. Those series have very interesting geometrical and arithmetic properties. For arithmetic subgroups of SL2R (with or without cusps), our construction allows us to define two natural rational structures on the space of cusp forms.
All Science Journal Classification (ASJC) codes
- Applied Mathematics