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

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. The proof relies on spectral theory of
Gamma\PSL(2,C).