Dirac’s comb is the Radon measure on R consisting of the sum of point measures at integers. It is the divisor of the real-rooted trigonometric polynomial sin 2πz and satisfies Poisson’s summation formula. Fourier quasicrystals with positive integer weights are generalizations of Dirac’s comb that satisfy a Poisson-type formula. In dimension one they coincide with divisors of real-rooted trigonometric polynomials. We discuss the multidimensional results in:
1. Lior Alon, Mario Kummer, Pavel Kurasov, Cynthia Vinzant, Higher dimensional Fourier quasicrystals from Lee–Yang varieties, Inventiones mathematicae 239 (2024) 321–376,
https://doi.org/10.1007/s00222-024-01307-8
2. Wayne M. Lawton, August K. Tsikh, Fourier Quasicrystals on R^n, The Journal of Geometric Analysis 35, 93 (2025) 50 pages,
https://doi.org/10.1007/s12220-025-01911-x