Partial solution of a conjecture of Schmutz
type: Item
instance of: scholarly article
title: Partial solution of a conjecture of Schmutz
zbMATH Open document ID: 0855.11017
DOI: 10.1007/BF01268932
author: Stefan Kühnlein
published in: Archiv der Mathematik
publication date: 1997-01-30T00:00:00Z
review text: It is proved that every non-arithmetic lattice in the Euclidean plane has every non-zero length shorter than the corresponding length of the \(A_2\)-lattice, when the lengths are numerated according to size (no multiplicities!) and when both lattices have the same covolume. This is done by elementary means. The conjecture of Schmutz is that the same fact holds for every lattice of the same covolume which is not isometric to the \(A_2\)-lattice. It does not seem to be treatable in the arithmetic case.
reviewed by: Stefan Kühnlein
Mathematics Subject Classification ID: 11E39
Mathematics Subject Classification ID: 11H06
Mathematics Subject Classification ID: 30F45
zbMATH DE Number: 938589
zbMATH Keywords: scalar squares of lattice points
zbMATH Keywords: Schmutz conjecture
zbMATH Keywords: non-arithmetic lattice
Wikidata QID: Q123015957
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf01268932
OpenAlex ID: W2063525508
description: scientific article; zbMATH DE number 938589