On the Local-Global Principle for Integral Apollonian-3 Circle Packings
Number Theory
2015-04-21 v2 Group Theory
Spectral Theory
Abstract
In this paper we study the integral properties of Apollonian-3 circle packings, which are variants of the standard Apollonian circle packings. Specifically, we study the reduction theory, formulate a local-global conjecture, and prove a density one version of this conjecture. Along the way, we prove a uniform spectral gap for congruence towers of the symmetry group.
Keywords
Cite
@article{arxiv.1312.4650,
title = {On the Local-Global Principle for Integral Apollonian-3 Circle Packings},
author = {Xin Zhang},
journal= {arXiv preprint arXiv:1312.4650},
year = {2015}
}
Comments
40 pages