Roots of Ehrhart Polynomials of Smooth Fano Polytopes

Abstract

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.

10 pages

References in corpus (4)

• An algorithm for the classification of smooth Fano polytopes
• Roots of Ehrhart polynomials of Gorenstein Fano polytopes
• The boundary volume of a lattice polytope
• Gale duality bounds for roots of polynomials with nonnegative coefficients

Cited by in corpus (2)

• Reflexive polytopes of higher index and the number 12
• Ehrhart polynomial roots of reflexive polytopes