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arXiv · 2407.11184

Higher Dimensional Fourier Quasicrystals from Lee-Yang Varieties

Lior Alon·Mario Kummer·Pavel Kurasov·Cynthia Vinzant
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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 $\mathbb{C}^n$, 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.

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Lior Alon, Mario Kummer, Pavel Kurasov, Cynthia Vinzant. 2024-07-15. Higher Dimensional Fourier Quasicrystals from Lee-Yang Varieties. https://doi.org/10.1007/s00222-024-01307-8

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