Ehrhart polynomial and Successive Minima

Details Ehrhart polynomial and Successive Minima Ehrhart polynomial and Successive Minima

2005-07-26

arxiv.org/abs/math/0507528v1

Mathematika 52 (2005), 1-16

Mathematics

Metric Geometry

Scientific paper

10.1112/S0025579300000292

We investigate the Ehrhart polynomial for the class of 0-symmetric convex lattice polytopes in Euclidean $n$-space $\mathbb{R}^n$. It turns out that the roots of the Ehrhart polynomial and Minkowski's successive minima are closely related by their geometric and arithmetic mean. We also show that the roots of lattice $n$-polytopes with or without interior lattice points differ essentially. Furthermore, we study the structure of the roots in the planar case. Here it turns out that their distribution reflects basic properties of lattice polygons.

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