Heimendahl, Arne, Marafioti, Aurelio, Thiemeyer, Antonia, Vallentin, Frank ORCID: 0000-0002-3205-4607 and Zimmermann, Marc Christian (2023). Critical Even Unimodular Lattices in the Gaussian Core Model. Int. Math. Res. Notices, 2023 (6). S. 5352 - 5397. OXFORD: OXFORD UNIV PRESS. ISSN 1687-0247

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Abstract

We consider even unimodular lattices that are critical for potential energy with respect to Gaussian potential functions in the manifold of lattices having point density 1. All even unimodular lattices up to dimension 24 are critical. We show how to determine the Morse index in these cases. While all these lattices are either local minima or saddle points, we find lattices in dimension 32, which are local maxima. Also starting from dimension 32 there are non-critical even unimodular lattices.

Item Type: Journal Article
Creators:
CreatorsEmailORCIDORCID Put Code
Heimendahl, ArneUNSPECIFIEDUNSPECIFIEDUNSPECIFIED
Marafioti, AurelioUNSPECIFIEDUNSPECIFIEDUNSPECIFIED
Thiemeyer, AntoniaUNSPECIFIEDUNSPECIFIEDUNSPECIFIED
Vallentin, FrankUNSPECIFIEDorcid.org/0000-0002-3205-4607UNSPECIFIED
Zimmermann, Marc ChristianUNSPECIFIEDUNSPECIFIEDUNSPECIFIED
URN: urn:nbn:de:hbz:38-658569
DOI: 10.1093/imrn/rnac164
Journal or Publication Title: Int. Math. Res. Notices
Volume: 2023
Number: 6
Page Range: S. 5352 - 5397
Date: 2023
Publisher: OXFORD UNIV PRESS
Place of Publication: OXFORD
ISSN: 1687-0247
Language: English
Faculty: Unspecified
Divisions: Unspecified
Subjects: no entry
Uncontrolled Keywords:
KeywordsLanguage
MathematicsMultiple languages
URI: http://kups.ub.uni-koeln.de/id/eprint/65856

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