On the number of perfect lattices
Journal de Théorie des Nombres de Bordeaux, Tome 30 (2018) no. 3, pp. 917-945.

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.

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.

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DOI : https://doi.org/10.5802/jtnb.1057
Classification : 11H55,  11T06,  20K01,  05B30,  05E30
Mots clés : Perfect lattice
@article{JTNB_2018__30_3_917_0,
     author = {Roland Bacher},
     title = {On the number of perfect lattices},
     journal = {Journal de Th\'eorie des Nombres de Bordeaux},
     pages = {917--945},
     publisher = {Soci\'et\'e Arithm\'etique de Bordeaux},
     volume = {30},
     number = {3},
     year = {2018},
     doi = {10.5802/jtnb.1057},
     language = {en},
     url = {https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.1057/}
}
Roland Bacher. On the number of perfect lattices. Journal de Théorie des Nombres de Bordeaux, Tome 30 (2018) no. 3, pp. 917-945. doi : 10.5802/jtnb.1057. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.1057/

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