Asymptotics of the number of waves on rational polyhedra
Number Theory
2022-12-27 v2 Mathematical Physics
Combinatorics
Metric Geometry
math.MP
Abstract
The problem of counting the number of waves arriving at the vertex of a polyhedron is motivated by physics. In the article it was solved for the case of Platonic solid using three nontrivial results from number theory. This growth turns out to be subexponential. Also we prove a subexponential upper bound for all polyhedra with rational total angles at vertices.
Cite
@article{arxiv.2112.12066,
title = {Asymptotics of the number of waves on rational polyhedra},
author = {Vsevolod L. Chernyshev and Alexey Rukhovich},
journal= {arXiv preprint arXiv:2112.12066},
year = {2022}
}
Comments
9 pages