A geometric study of circle packings and ideal class groups
Number Theory
2022-02-23 v1
Abstract
A family of fractal arrangements of circles is introduced for each imaginary quadratic field . Collectively, these arrangements contain (up to an affine transformation) every set of circles in the extended complex plane with integral curvatures and Zariski dense symmetry group. When that set is a circle packing, we show how the ambient structure of our arrangement gives a geometric criterion for satisfying the almost local-global principle. Connections to the class group of are also explored. Among them is a geometric property that guarantees certain ideal classes are group generators.
Cite
@article{arxiv.2202.10530,
title = {A geometric study of circle packings and ideal class groups},
author = {Daniel Martin},
journal= {arXiv preprint arXiv:2202.10530},
year = {2022}
}
Comments
23 pages, 6 figures