Effective Bisector Estimate with Application to Apollonian Circle Packings
Effective Bisector Estimate with Application to Apollonian Circle Packings
Let Γ<PSL(2,C) be a geometrically finite nonelementary 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 …