The hyperbolic lattice point count in infinite volume with applications to sieves
The hyperbolic lattice point count in infinite volume with applications to sieves
We develop novel techniques using abstract operator theory to obtain asymptotic formulae for lattice counting problems on infinite-volume hyperbolic manifolds, with error terms which are uniform as the lattice moves through "congruence" subgroups. We give the following application to the theory of affine linear sieves. In the spirit of Fermat, …