We derive sufficient conditions for an atomic measure ∑λ∈Λ​mλ​δλ​, where Λ⊂Rn,mλ​ are positive integers, and δλ​ is the point measure at
λ, to be a Fourier quasicrystal, and suggest why they may also be
necessary. These conditions extend the necessary and sufficient conditions
derived by Lev, Olevskii, and Ulanovskii for n=1. Our methods exploit the
toric geometry relation between Grothendieck residues and Newton polytopes
derived by Gelfond and Khovanskii.Comment: 17 page