S-extremal strongly modular lattices
Journal de Théorie des Nombres de Bordeaux, Tome 19 (2007) no. 3, pp. 683-701.

Un réseau fortement modulaire est dit s-extrémal, s’il maximise le minimum du réseau et son ombre simultanément. La dimension des réseaux s-extrémaux dont le minimum est pair peut être bornée par la théorie des formes modulaires. En particulier de tels réseaux sont extrémaux.

S-extremal strongly modular lattices maximize the minimum of the lattice and its shadow simultaneously. They are a direct generalization of the s-extremal unimodular lattices defined in [6]. If the minimum of the lattice is even, then the dimension of an s-extremal lattices can be bounded by the theory of modular forms. This shows that such lattices are also extremal and that there are only finitely many s-extremal strongly modular lattices of even minimum.

@article{JTNB_2007__19_3_683_0,
     author = {Nebe, Gabriele and Schindelar, Kristina},
     title = {S-extremal strongly modular lattices},
     journal = {Journal de Th\'eorie des Nombres de Bordeaux},
     pages = {683--701},
     publisher = {Universit\'e Bordeaux 1},
     volume = {19},
     number = {3},
     year = {2007},
     doi = {10.5802/jtnb.608},
     mrnumber = {2388794},
     zbl = {1196.11097},
     language = {en},
     url = {http://www.numdam.org/articles/10.5802/jtnb.608/}
}
Nebe, Gabriele; Schindelar, Kristina. S-extremal strongly modular lattices. Journal de Théorie des Nombres de Bordeaux, Tome 19 (2007) no. 3, pp. 683-701. doi : 10.5802/jtnb.608. http://www.numdam.org/articles/10.5802/jtnb.608/

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