Harmonic analysis, Ergodic theory and Counting for thin groups
arXiv:1208.4148
Abstract
For a geometrically finite group Gamma of G=SO(n,1), we survey recent developments on counting and equidistribution problems for orbits of Gamma in a homogeneous space H\G where H is trivial, symmetric or horospherical. Main applications are found in an affine sieve on orbits of thin groups as well as in sphere counting problems for sphere packings invariant under a geometrically finite group. In our sphere counting problems, spheres can be ordered with respect to a general conformal metric.
33 pages, minor revision
References in corpus (6)
- Counting, Mixing and Equidistribution of horospheres in geometrically finite rank one locally symmetric manifolds
- Counting visible circles on the sphere and Kleinian groups
- Lifting, restricting and sifting integral points on affine homogeneous varieties
- Effective Circle Count for Apollonian packings and Closed horospheres
- Sieve in discrete groups, especially sparse
- Ergodicity of unipotent flows and Kleinian groups