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arXiv · 1204.5498

Effective bisector estimate with application to Apollonian circle packings

Ilya Vinogradov
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Abstract

Let Γ<\PSL(2,\C) be a geometrically finite non-elementary discrete subgroup, and let its critical exponent δ be greater than 1. We use representation theory of \PSL(2,\C) to prove an effective bisector counting theorem for Γ, which allows counting the number of points of Γ in general expanding regions in \PSL(2,\C) and provides an explicit error term. We apply this theorem to give power savings in the Apollonian circle packing problem and related counting problems.

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Ilya Vinogradov. 2012-04-24. Effective bisector estimate with application to Apollonian circle packings. https://arxiv.org/abs/1204.5498

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