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arXiv · 1208.4148

Harmonic analysis, Ergodic theory and Counting for thin groups

Hee Oh
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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.

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Hee Oh. 2012-08-21. Harmonic analysis, Ergodic theory and Counting for thin groups. https://arxiv.org/abs/1208.4148

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