Effective bisector estimate for PSL(2,C) with applications to circle packings

Effective bisector estimate for PSL(2,C) with applications to circle packings

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Ilya Vinogradov, Princeton University
Fine Hall 601

Let Gamma be a non-elementary discrete geometrically finite subgroup of PSL(2,C). Under the assumption that the critical exponent of Gamma is greater than 1 we prove an effective bisector counting theorem for Gamma. We then apply this Theorem to the Apollonian circle packing problem to get power savings and to compute the overall constant. The proof relies on spectral theory of Gamma\PSL(2,C).