by Bey, C., Henk, M., Wills, J. M..
Series: 2006-30, Preprints
We determine lattice polytopes of smallest volume with a given
number of interior lattice points. We show that the Ehrhart
polynomials of those with one interior lattice point have
largest roots with norm of order $n^2$, where $n$ is the
dimension. This improves on the previously best known bound
$n$ and complements a recent result of Braun  where it is
shown that the norm of a root of a Ehrhart polynomial is at
most of order $n^2$.
For the class of 0-symmetric lattice polytopes we present
a conjecture on the smallest volume for a given number of
interior lattice points and prove the conjecture for
We further give a characaterisation of the roots of Ehrhart
polynomials in the 3-dimensional case and we classify for
$n \leq 4$ all lattice polytopes whose roots of their
Ehrhart polynomials have all real part -1/2. These polytopes
belong to the class of reflexive polytopes.
Lattice polytopes, Ehrhart polynomial, reflexive polytopes