# Roots of Ehrhart Polynomials of Smooth Fano Polytopes - Mathematics > Combinatorics

Abstract: V. Golyshev conjectured that for any smooth polytope P of dimension at mostfive, the roots $z\in\C$ of the Ehrhart polynomial for P have real part equalto -1-2. An elementary proof is given, and in each dimension the roots aredescribed explicitly. We also present examples which demonstrate that thisresult cannot be extended to dimension six.

Author: Gábor Hegedüs, Alexander M. Kasprzyk

Source: https://arxiv.org/