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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 Cn\mathbb{C}^n, 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}
}