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arXiv · 1202.1067

Effective Circle Count for Apollonian packings and Closed horospheres

Min Lee·Hee Oh
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Abstract

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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Min Lee, Hee Oh. 2012-02-06. Effective Circle Count for Apollonian packings and Closed horospheres. https://arxiv.org/abs/1202.1067

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