Two-dimensional lattices with few distances

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Title: Two-dimensional lattices with few distances
Authors: Moree, Pieter
Osburn, Robert
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Date: Jun-2006
Online since: 2016-09-16T11:42:32Z
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.
Type of material: Journal Article
Publisher: European Mathematical Society
Journal: L'Enseignement Mathematique
Volume: 52
Issue: 2
Start page: 361
End page: 380
Keywords: Schmutz Schaller conjecturePopulation fractionBinary quadratic formsErdős number
DOI: 10.5169/seals-2239
Language: en
Status of Item: Peer reviewed
Appears in Collections:Mathematics and Statistics Research Collection

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