Higher dimensional Fourier quasicrystals from Lee–Yang varieties
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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.
Date issued
2024-12-16Department
Massachusetts Institute of Technology. Department of MathematicsJournal
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