Two-dimensional lattices with few distances
Number Theory
2008-02-01 v2
Abstract
We prove that of all two-dimensional lattices of covolume 1 the hexagonal lattice has asymptotically the fewest distances. An analogous result for dimensions 3 to 8 was proved in 1991 by Conway and Sloane. Moreover, we give a survey of some related literature, in particular progress on a conjecture from 1995 due to Schmutz Schaller.
Cite
@article{arxiv.math/0604163,
title = {Two-dimensional lattices with few distances},
author = {Pieter Moree and Robert Osburn},
journal= {arXiv preprint arXiv:math/0604163},
year = {2008}
}
Comments
21 pages, final version, accepted for publication in L'Enseignement Math\'ematique