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.
@article{JTNB_2007__19_3_683_0,
author = {Gabriele Nebe and Kristina Schindelar},
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 = {https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.608/}
}
TY - JOUR AU - Gabriele Nebe AU - Kristina Schindelar TI - S-extremal strongly modular lattices JO - Journal de théorie des nombres de Bordeaux PY - 2007 SP - 683 EP - 701 VL - 19 IS - 3 PB - Université Bordeaux 1 UR - https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.608/ UR - https://www.ams.org/mathscinet-getitem?mr=2388794 UR - https://zbmath.org/?q=an%3A1196.11097 UR - https://doi.org/10.5802/jtnb.608 DO - 10.5802/jtnb.608 LA - en ID - JTNB_2007__19_3_683_0 ER -
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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