The sphere packing problem in dimension $24$

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 May 2017Embargo end date: 01 Jan 2016Publisher:Annals of MathematicsJournal:Annals of Mathematics, volume 185 (issn: 0003-486X,

Copyright policy )Funded by:NSF | Automorphic Forms on High..., NSF | TWC: Small: Automorphic F...

Authors: Cohn, H.; Kumar, A.; Miller, S.; Radchenko, D. ; https://orcid.org/0000-0003-1457-6214; Viazovska, M.;

doi: 10.4007/annals.2017.185.3.8 , 10.48550/arxiv.1603.06518

arXiv: 1603.06518

handle: 21.11116/0000-0004-08A5-9 , 21.11116/0000-0004-08A6-8 , 21.11116/0000-0004-08A3-B

The sphere packing problem in dimension $24$

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Abstract

Building on Viazovska's recent solution of the sphere packing problem in eight dimensions, we prove that the Leech lattice is the densest packing of congruent spheres in twenty-four dimensions and that it is the unique optimal periodic packing. In particular, we find an optimal auxiliary function for the linear programming bounds, which is an analogue of Viazovska's function for the eight-dimensional case.

17 pages

Related Organizations

Humboldt-Universität zu Berlin
Germany
Max Planck Institute for Mathematics
Germany
Microsoft (United States)
United States
Stony Brook University Hospital
United States
Max Planck Society
Germany

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Keywords

Mathematics - Number Theory, Mathematics - Metric Geometry, FOS: Mathematics, Metric Geometry (math.MG), Number Theory (math.NT)

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