Higher dimensional Fourier quasicrystals from Lee–Yang varieties
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222_2024_1307_ReferencePDF.pdf
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Author(s)
Alon, Lior
Kummer, Mario
Kurasov, Pavel
Vinzant, Cynthia
Date Issued
December 16, 2024
Journal
Inventiones mathematicae
Publisher
Springer Berlin Heidelberg
Citation
Alon, L., Kummer, M., Kurasov, P. et al. Higher dimensional Fourier quasicrystals from Lee–Yang varieties. Invent. math. 239, 321–376 (2025).
Version
Author's final manuscript
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 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.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
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DOI of Published Version
https://doi.org/10.1007/s00222-024-01307-8
