S-extremal strongly modular lattices
Gabriele Nebe1; Kristina Schindelar1
1 Lehrstuhl D für Mathematik RWTH Aachen 52056 Aachen, Germany
Journal de Théorie des Nombres de Bordeaux, Volume 19 (2007) no. 3, pp. 683-701.

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.

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.

Received:
Published online:
DOI: 10.5802/jtnb.608
Gabriele Nebe 1; Kristina Schindelar 1

1 Lehrstuhl D für Mathematik RWTH Aachen 52056 Aachen, Germany 
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Gabriele Nebe; Kristina Schindelar. S-extremal strongly modular lattices. Journal de Théorie des Nombres de Bordeaux, Volume 19 (2007) no. 3, pp. 683-701. doi : 10.5802/jtnb.608. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.608/

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