Asymptotic Density of Apollonian-Type Packings
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.
- Publication:
-
arXiv e-prints
- Pub Date:
- August 2021
- DOI:
- 10.48550/arXiv.2108.06358
- arXiv:
- arXiv:2108.06358
- Bibcode:
- 2021arXiv210806358L
- Keywords:
-
- Mathematics - Number Theory;
- 11A05;
- 11F06;
- 22E40