We show that the number of non-similar perfect -dimensional lattices satisfies eventually the inequalities for arbitrary small strictly positive .
Le nombre de classes de similitude de réseaux parfaits en dimension vérifie asymptotiquement les inégalités pour arbitrairement petit.
Revised:
Accepted:
Published online:
DOI: 10.5802/jtnb.1057
Keywords: 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}, mrnumber = {3938634}, language = {en}, url = {https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.1057/} }
TY - JOUR AU - Roland Bacher TI - On the number of perfect lattices JO - Journal de théorie des nombres de Bordeaux PY - 2018 SP - 917 EP - 945 VL - 30 IS - 3 PB - Société Arithmétique de Bordeaux UR - https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.1057/ DO - 10.5802/jtnb.1057 LA - en ID - JTNB_2018__30_3_917_0 ER -
%0 Journal Article %A Roland Bacher %T On the number of perfect lattices %J Journal de théorie des nombres de Bordeaux %D 2018 %P 917-945 %V 30 %N 3 %I Société Arithmétique de Bordeaux %U https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.1057/ %R 10.5802/jtnb.1057 %G en %F JTNB_2018__30_3_917_0
Roland Bacher. 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. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.1057/
[1] Constructions of some perfect integral lattices with minimum 4, J. Théor. Nombres Bordx, Volume 27 (2015) no. 3, pp. 655-687 | DOI | Numdam | MR | Zbl
[2] Spherical -designs and lattices from Abelian groups, Discrete Comput. Geom. (2017) | DOI
[3] On lattices generated by finite abelian groups, SIAM J. Discrete Math., Volume 29 (2015) no. 1, pp. 382-404 | DOI | MR | Zbl
[4] Sphere Packings, Lattices and Groups, Grundlehren der Mathematischen Wissenschaften, 290, Springer, 1999 | MR | Zbl
[5] Classification of eight-dimensional perfect forms, Electron. Res. Announc. Am. Math. Soc., Volume 13 (2007), pp. 21-32 | MR | Zbl
[6] Alternative formulae for the number of sublattices, Acta Crystallogr., Volume 53 (1997) no. 6, pp. 807-808 | DOI | MR | Zbl
[7] On classifying Minkowskian sublattices. With an Appendix by Mathieu Dutour Sikirić, Math. Comput., Volume 81 (2012) no. 278, pp. 1063-1092 | Zbl
[8] Arithmetic of quadratic forms, Cambridge Tracts in Mathematics, 106, Cambridge University Press, 1993 | MR | Zbl
[9] Les réseaux parfaits des espaces euclidiens, Masson, 1996 (an English translation has been published by Springer) | Zbl
[10] Geometrie der Zahlen, Teubner, 1896 | Zbl
[11] Boris Venkovâs theory of lattices and spherical designs, Diophantine methods, lattices, and arithmetic theory of quadratic forms (BIRS, 2011) (Contemporary Mathematics), Volume 587, American Mathematical Society, 2013, pp. 1-19 | DOI | MR | Zbl
[12] Perfect forms and the Vandiver conjecture, J. Reine Angew. Math., Volume 517 (1999), pp. 209-221 | DOI | MR | Zbl
[13] Gaussian binomials and the number of sublattices, Acta Crystallogr., Volume 62 (2006) no. 5, pp. 409-410 | DOI | MR | Zbl
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