Effective Circle Count for Apollonian packings and Closed horospheres

Details Effective Circle Count for Apollonian packings and Closed horospheres Effective Circle Count for Apollonian packings and Closed horospheres

2012-02-06

arxiv.org/abs/1202.1067v3

Mathematics

Dynamical Systems

2 figures, 40 pages, the paper with the same title, and the paper titled "Effective equidistribution of closed horocycles for

Scientific paper

The main result of this paper is an effective count for Apollonian circle packings that are either bounded or contain two parallel lines. We obtain this by proving an effective equidistribution of closed horospheres in the unit tangent bundle of a geometrically finite hyperbolic 3-manifold of infinite volume, whose fundamental group has critical exponent bigger than 1. We also discuss applications to Affine sieves. Analogous results for surfaces are treated as well.

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