2000/08/03 by Oleg Pikhurko, Pikhurko, Oleg
Mathematics · #52B20 #Algebraic Geometry and Number Theory #Analytic and geometric function theory #Combinatorics (math.CO) #FOS: Mathematics #Metric Geometry (math.MG) #Number Theory (math.NT) #math.CO #math.MG #math.NT #msc:52B20
paper · pdf · doi:10.48550/arxiv.math/0008028
14 pages (paper) + 22 pages (C code) Submitted to Mathematika
openalex publication_date 2000/08/03 · arxiv created 2000/10/02 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We show that, if the interior of a lattice d-polytope P contains at least one lattice point, then it contains a lattice point whose coefficient of asymmetry with respect to P is at most b for some number b depending on d only. As an application, we obtain new upper bounds on the volume of a lattice polytope given the number of lattice points in its interior.