On the Local-Global Conjecture for integral Apollonian gaskets
Number Theory
2013-05-15 v2
Abstract
We prove that a set of density one satisfies the local-global conjecture for integral Apollonian gaskets. That is, for a fixed integral, primitive Apollonian gasket, almost every (in the sense of density) admissible (passing local obstructions) integer is the curvature of some circle in the gasket.
Cite
@article{arxiv.1205.4416,
title = {On the Local-Global Conjecture for integral Apollonian gaskets},
author = {Jean Bourgain and Alex Kontorovich},
journal= {arXiv preprint arXiv:1205.4416},
year = {2013}
}
Comments
64 pages, 3 figures; Appendix by Peter Varju