Roots of Ehrhart polynomials of smooth Fano polytopes - Hegedüs, Gábor; Kasprzyk, Alexander M. (Springer-Verlag, 2011)
V. Golyshev conjectured that for any smooth polytope P of dimension at most five, the roots $z\in\C$ of the Ehrhart polynomial for P have real part equal to -1/2. An elementary proof is given, and in each dimension the roots are described explicitly. We also present examples which demonstrate that this result cannot be extended to dimension six.