Higher dimensional Fourier quasicrystals from Lee-Yang varieties
成果类型：
Article
署名作者：
Alon, Lior; Kummer, Mario; Kurasov, Pavel; Vinzant, Cynthia
署名单位：
Massachusetts Institute of Technology (MIT); Technische Universitat Dresden; Stockholm University; University of Washington; University of Washington Seattle
刊物名称：
INVENTIONES MATHEMATICAE
ISSN/ISSBN：
0020-9910
DOI：
10.1007/s00222-024-01307-8
发表日期：
2025
页码：
321-376
关键词：
摘要：
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\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}${\mathbb{C}}<^>{n}$\end{document}, 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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