Asymptotic Density of Apollonian-Type Packings

Published 13 Aug 2021 in math.NT | (2108.06358v1)

Abstract: We consider two seemingly unconnected problems: first, under what circumstances are arithmetic groups like SL(2,O) generated by elementary matrices; second, when do certain classes of circle/sphere packings fill up space? We show that these are in fact deeply related, leading to some new results, new proofs of old results, and interesting conjectures.

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