Similarity submodules and root systems in four dimensions

Authors
Baake, M Moody, RV
Citation
M. Baake et Rv. Moody, Similarity submodules and root systems in four dimensions, CAN J MATH, 51(6), 1999, pp. 1258-1276
Citations number
37
Categorie Soggetti
Mathematics
Journal title
CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES
ISSN journal
0008414X → ACNP
Volume
51
Issue
6
Year of publication
1999
Pages
1258 - 1276
Database
ISI
SICI code
0008-414X(199912)51:6<1258:SSARSI>2.0.ZU;2-Y
Abstract
Lattices and Z-modules in Euclidean space possess an infinitude of subsets that are images of the original set under similarity transformation. We cla ssify such self-similar images according to their indices for certain 4D ex amples that are related to 4D root systems, both crystallographic and nan-c rystallographic. We encapsulate their statistics in terms of Dirichlet seri es generating functions and derive same of their asymptotic properties.