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A Lee-Yang polynomial $ p(z_{1},\ldots,z_{n}) $ is a polynomial that has nozeros in the polydisc $ \mathbb{D}^{n} $ and its inverse $(\mathbb{C}\setminus\overline{\mathbb{D}})^{n} $. We show that any real-rootedexponential polynomial of the form $f(x) = \sum_{j=0}^s c_j e^{\lambda_j x}$can be written as the restriction of a Lee-Yang polynomial to a positive linein the torus. Together with previous work by Olevskii and Ulanovskii, thisimplies that the Kurasov-Sarnak construction of $ \mathbb{N} $-valued Fourierquasicrystals from stable polynomials comprises every possible $ \mathbb{N}$-valued Fourier quasicrystal.

Every real-rooted exponential polynomial is the restriction of a Lee-Yang polynomial