The Local-Global Principle for Integral Soddy Sphere Packings
Number Theory
2017-06-16 v2
Abstract
Fix an integral Soddy sphere packing P. Let K be the set of all curvatures in P. A number n is called represented if n is in K, that is, if there is a sphere in P with curvature equal to n. A number n is called admissible if it is everywhere locally represented, meaning that n is in K(mod q) for all q. It is shown that every sufficiently large admissible number is represented.
Cite
@article{arxiv.1208.5441,
title = {The Local-Global Principle for Integral Soddy Sphere Packings},
author = {Alex Kontorovich},
journal= {arXiv preprint arXiv:1208.5441},
year = {2017}
}
Comments
34 pages, 5 figures