Configurations of rank-${40r}$ extremal even unimodular lattices (${r=1,2,3}$)

Kominers, Scott Duke; Abel, Zachary

doi:10.5802/jtnb.632

Configurations of rank-

40 r

extremal even unimodular lattices (

r = 1, 2, 3

)

Kominers, Scott Duke ¹; Abel, Zachary ²

¹ Department of Mathematics Harvard University c/o 8520 Burning Tree Road Bethesda, Maryland, 20817, USA
² Department of Mathematics Harvard University c/o 17134 Earthwind Drive Dallas, Texas, 75248, USA

Journal de théorie des nombres de Bordeaux, Volume 20 (2008) no. 2, pp. 365-371.

Abstract
Résumé

We show that if $L$ is an extremal even unimodular lattice of rank $40 r$ with $r = 1, 2, 3$ , then $L$ is generated by its vectors of norms $4 r$ and $4 r + 2$ . Our result is an extension of Ozeki’s result for the case $r = 1$ .

Nous montrons que, si $L$ est un réseau unimodulaire pair extrémal de rang $40 r$ avec $r = 1, 2, 3$ , alors $L$ est engendré par ses vecteurs de normes $4 r$ et $4 r + 2$ . Notre résultat est une extension de celui d’Ozeki pour le cas $r = 1$ .

EuDML MR Zbl

DOI: 10.5802/jtnb.632

Mots-clés : Even unimodular lattices, extremal lattices, weighted theta series

Author's affiliations:

Kominers, Scott Duke ¹; Abel, Zachary ²

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     author = {Kominers, Scott Duke and Abel, Zachary},
     title = {Configurations of rank-${40r}$ extremal even unimodular lattices (${r=1,2,3}$)},
     journal = {Journal de th\'eorie des nombres de Bordeaux},
     pages = {365--371},
     publisher = {Universit\'e Bordeaux 1},
     volume = {20},
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     year = {2008},
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Kominers, Scott Duke; Abel, Zachary. Configurations of rank-${40r}$ extremal even unimodular lattices (${r=1,2,3}$). Journal de théorie des nombres de Bordeaux, Volume 20 (2008) no. 2, pp. 365-371. doi : 10.5802/jtnb.632. http://archive.numdam.org/articles/10.5802/jtnb.632/

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