Geodesic
The sphere packing problem in dimension $24$
Henry Cohn1 ; Abhinav Kumar2 ; Stephen D. Miller3 ; Danylo Radchenko4 ; Maryna Viazovska5
1 Microsoft Research New England, Cambridge, MA
2 Stony Brook University, Stony Brook, NY
3 Rutgers University, Piscataway, NJ
4 Max Planck Institute for Mathematics, Bonn, Germany
5 Berlin Mathematical School and Humboldt University of Berlin, Berlin, Germany
Annals of mathematics, Tome 185 (2017) no. 3, pp. 1017-1033.

Voir la notice de l'article provenant de la source Annals of Mathematics website

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.
Computer code for verifying the calculations in this paper is is available at the following location:
https://doi.org/10.4007/annals.2017.185.3.8.code
DOI : 10.4007/annals.2017.185.3.8

Henry Cohn 1 ; Abhinav Kumar 2 ; Stephen D. Miller 3 ; Danylo Radchenko 4 ; Maryna Viazovska 5

1 Microsoft Research New England, Cambridge, MA
2 Stony Brook University, Stony Brook, NY
3 Rutgers University, Piscataway, NJ
4 Max Planck Institute for Mathematics, Bonn, Germany
5 Berlin Mathematical School and Humboldt University of Berlin, Berlin, Germany 
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Henry Cohn; Abhinav Kumar; Stephen D. Miller; Danylo Radchenko; Maryna Viazovska. The sphere packing problem in dimension $24$. Annals of mathematics, Tome 185 (2017) no. 3, pp. 1017-1033. doi : 10.4007/annals.2017.185.3.8. http://geodesic.mathdoc.fr/articles/10.4007/annals.2017.185.3.8/

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