Similarity submodules and root systems in four dimensions
Metric Geometry
2007-05-23 v1 Mathematical Physics
math.MP
Number Theory
Abstract
Lattices and Z-modules in Euclidean space possess an infinitude of subsets that are images of the original set under similarity transformation. We classify such self-similar images according to their indices for certain 4D examples that are related to 4D root systems, both crystallographic and non-crystallographic. We encapsulate their statistics in terms of Dirichlet series generating functions and derive some of their asymptotic properties.
Cite
@article{arxiv.math/9904028,
title = {Similarity submodules and root systems in four dimensions},
author = {Michael Baake and Robert V. Moody},
journal= {arXiv preprint arXiv:math/9904028},
year = {2007}
}
Comments
24 pages; written for a special issue of Can. J. Math. in honour of H.S.M. Coxeter