Higher Dimensional Fourier Quasicrystals from Lee-Yang Varieties
Mathematical Physics
2026-01-30 v1 Algebraic Geometry
Complex Variables
Functional Analysis
math.MP
Abstract
In this paper, we construct Fourier quasicrystals with unit masses in arbitrary dimensions. This generalizes a one-dimensional construction of Kurasov and Sarnak. To do this, we employ a class of complex algebraic varieties avoiding certain regions in , which generalize hypersurfaces defined by Lee-Yang polynomials. We show that these are Delone almost periodic sets that have at most finite intersection with every discrete periodic set.
Keywords
Cite
@article{arxiv.2407.11184,
title = {Higher Dimensional Fourier Quasicrystals from Lee-Yang Varieties},
author = {Lior Alon and Mario Kummer and Pavel Kurasov and Cynthia Vinzant},
journal= {arXiv preprint arXiv:2407.11184},
year = {2026}
}