On the number of perfect lattices
Journal de théorie des nombres de Bordeaux, Volume 30 (2018) no. 3, pp. 917-945.

We show that the number p d of non-similar perfect d-dimensional lattices satisfies eventually the inequalities e d 1-ϵ <p d <e d 3+ϵ for arbitrary small strictly positive ϵ.

Le nombre p d de classes de similitude de réseaux parfaits en dimension d vérifie asymptotiquement les inégalités e d 1-ϵ <p d <e d 3+ϵ pour ϵ>0 arbitrairement petit.

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Accepted:
Published online:
DOI: 10.5802/jtnb.1057
Classification: 11H55, 11T06, 20K01, 05B30, 05E30
Keywords: Perfect lattice
Bacher, Roland 1

1 Institut Fourier Univ. Grenoble Alpes, CNRS 38000 Grenoble, France
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Bacher, Roland. On the number of perfect lattices. Journal de théorie des nombres de Bordeaux, Volume 30 (2018) no. 3, pp. 917-945. doi : 10.5802/jtnb.1057. http://www.numdam.org/articles/10.5802/jtnb.1057/

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