Geometry and combinatoric of Minkowski-Voronoi 3-dimensional continued fractions

Karpenkov, Oleg ORCID: 0000-0002-3358-6998 and Ustinov, Alexey (2017) Geometry and combinatoric of Minkowski-Voronoi 3-dimensional continued fractions. Journal of Number Theory, 176. pp. 375-419.

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Abstract

In this paper we investigate the combinatorial structure of 3-dimensional Minkowski–Voronoi continued fractions. Our main goal is to prove the asymptotic stability of Minkowski–Voronoi complexes in special two-parametric families of rank-1 lattices. In addition we construct explicitly the complexes for the case of White's rank-1 lattices and provide with a hypothetic description in a more complicated settings

Item Type:	Article
Uncontrolled Keywords:	Minkowski minima, Minkowski-Voronoi continued fraction, Lattice geometry
Depositing User:	Symplectic Admin
Date Deposited:	02 Feb 2017 11:38
Last Modified:	19 Jan 2023 07:19
DOI:	10.1016/j.jnt.2016.12.005
Related URLs:	Author Publisher
URI:	https://livrepository.liverpool.ac.uk/id/eprint/3005522