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.

DOI : 10.5802/jtnb.608
Nebe, Gabriele 1 ; Schindelar, Kristina 1

1 Lehrstuhl D für Mathematik RWTH Aachen 52056 Aachen, Germany
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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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