Configurations of rank-$40r$ extremal even unimodular lattices ($r=1,2,3$)
Journal de théorie des nombres de Bordeaux, Volume 20 (2008) no. 2, p. 365-371

We show that if $L$ is an extremal even unimodular lattice of rank $40r$ with $r=1,2,3$, then $L$ is generated by its vectors of norms $4r$ and $4r+2$. 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 $40r$ avec $r=1,2,3$, alors $L$ est engendré par ses vecteurs de normes $4r$ et $4r+2$. Notre résultat est une extension de celui d’Ozeki pour le cas $r=1$.

DOI : https://doi.org/10.5802/jtnb.632
Keywords: Even unimodular lattices, extremal lattices, weighted theta series
@article{JTNB_2008__20_2_365_0,
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},
publisher = {Universit\'e Bordeaux 1},
volume = {20},
number = {2},
year = {2008},
pages = {365-371},
doi = {10.5802/jtnb.632},
zbl = {1185.11044},
mrnumber = {2477509},
zbl = {pre05543167},
language = {en},
url = {http://www.numdam.org/item/JTNB_2008__20_2_365_0}
}

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://www.numdam.org/item/JTNB_2008__20_2_365_0/

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