Geodesic
Configurations of rank-40r extremal even unimodular lattices (r=1,2,3)
Kominers, Scott Duke1  ; Abel, Zachary2
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, Tome 20 (2008) no. 2, pp. 365-371

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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 : 10.5802/jtnb.632
Keywords: Even unimodular lattices, extremal lattices, weighted theta series

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 
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     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},
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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, Tome 20 (2008) no. 2, pp. 365-371. doi: 10.5802/jtnb.632

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