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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