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The sphere packing problem in dimension 24

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arxiv 1603.06518 v3 pith:HV7GQJPM submitted 2016-03-21 math.NT math.MG

Henry Cohn , Abhinav Kumar , Stephen D. Miller , Danylo Radchenko , Maryna Viazovska This is my paper · ORCID
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keywords packingdimensionsfunctionoptimalproblemsphereviazovskaanalogue
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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.

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  1. Variations on five-dimensional sphere packings

    math.MG 2024-12 accept novelty 7.0 of 10

    New non-isometric kissing configurations are constructed in dimensions 5 and 9, and the uniform 5D packings containing the known kissing configurations are classified.

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