Asymptotics of the number of waves on rational polyhedra

Vsevolod L. Chernyshev; Alexey Rukhovich

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arXiv · 2112.12066

Asymptotics of the number of waves on rational polyhedra

Vsevolod L. Chernyshev·Alexey Rukhovich

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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.

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Vsevolod L. Chernyshev, Alexey Rukhovich. 2021-12-13. Asymptotics of the number of waves on rational polyhedra. https://arxiv.org/abs/2112.12066

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