Geodesic
Optimality and uniqueness of the Leech lattice among lattices
Henry Cohn1 ; Abhinav Kumar2
1 Microsoft Research New England<br/>One Memorial Drive<br/>Cambridge, MA 02142<br/>United States
2 Department of Mathematics<br/>Room 2-169<br/>Massachusetts Institute of Technology<br/>Cambridge, MA 02139<br/>United States
Annals of mathematics, Tome 170 (2009) no. 3, pp. 1003-1050.

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

We prove that the Leech lattice is the unique densest lattice in $\mathbb{R}^{24}$. The proof combines human reasoning with computer verification of the properties of certain explicit polynomials. We furthermore prove that no sphere packing in $\mathbb{R}^{24}$ can exceed the Leech lattice’s density by a factor of more than $1+1.65\cdot 10^{-30}$, and we give a new proof that $E_8$ is the unique densest lattice in $\mathbb{R}^8$.
DOI : 10.4007/annals.2009.170.1003

Henry Cohn 1 ; Abhinav Kumar 2

1 Microsoft Research New England<br/>One Memorial Drive<br/>Cambridge, MA 02142<br/>United States
2 Department of Mathematics<br/>Room 2-169<br/>Massachusetts Institute of Technology<br/>Cambridge, MA 02139<br/>United States 
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Henry Cohn; Abhinav Kumar. Optimality and uniqueness of the Leech lattice among lattices. Annals of mathematics, Tome 170 (2009) no. 3, pp. 1003-1050. doi : 10.4007/annals.2009.170.1003. http://geodesic.mathdoc.fr/articles/10.4007/annals.2009.170.1003/

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