The strongly perfect lattices of dimension 10
Journal de théorie des nombres de Bordeaux, Tome 12 (2000) no. 2, pp. 503-518.

Cet article donne une classification des réseaux fortement parfaits en dimension 10. A similitude près il y a deux tels réseaux, K10' et son réseau dual.

This paper classifies the strongly perfect lattices in dimension 10. There are up to similarity two such lattices, K10' and its dual lattice.

@article{JTNB_2000__12_2_503_0,
     author = {Nebe, Gabriele and Venkov, Boris},
     title = {The strongly perfect lattices of dimension $10$},
     journal = {Journal de th\'eorie des nombres de Bordeaux},
     pages = {503--518},
     publisher = {Universit\'e Bordeaux I},
     volume = {12},
     number = {2},
     year = {2000},
     mrnumber = {1823200},
     zbl = {0997.11049},
     language = {en},
     url = {https://www.numdam.org/item/JTNB_2000__12_2_503_0/}
}
TY  - JOUR
AU  - Nebe, Gabriele
AU  - Venkov, Boris
TI  - The strongly perfect lattices of dimension $10$
JO  - Journal de théorie des nombres de Bordeaux
PY  - 2000
SP  - 503
EP  - 518
VL  - 12
IS  - 2
PB  - Université Bordeaux I
UR  - https://www.numdam.org/item/JTNB_2000__12_2_503_0/
LA  - en
ID  - JTNB_2000__12_2_503_0
ER  - 
%0 Journal Article
%A Nebe, Gabriele
%A Venkov, Boris
%T The strongly perfect lattices of dimension $10$
%J Journal de théorie des nombres de Bordeaux
%D 2000
%P 503-518
%V 12
%N 2
%I Université Bordeaux I
%U https://www.numdam.org/item/JTNB_2000__12_2_503_0/
%G en
%F JTNB_2000__12_2_503_0
Nebe, Gabriele; Venkov, Boris. The strongly perfect lattices of dimension $10$. Journal de théorie des nombres de Bordeaux, Tome 12 (2000) no. 2, pp. 503-518. https://www.numdam.org/item/JTNB_2000__12_2_503_0/

[BaV] C. Bachoc, B. Venkov, Modular forms, lattices and spherical designs. In [EM]. | Zbl

[Cas] J.W.S. Cassels, Rational quadratic forms. Academic Press (1978). | MR | Zbl

[CoS] J.H. Conway, N.J A. Sloane, Sphere Packings, Lattices and Groups. 3rd edition, Springer-Verlag (1998). | Zbl

[CoS] J.H. Conway, N.J.A. Sloane, On Lattices Equivalent to Their Duals. J. Number Theory 48 (1994), 373-382. | MR | Zbl

[EM] Réseaux euclidiens, designs sphériques et groupes. Edited by J. Martinet. Enseignement des Mathématiques, monographie 37, to appear. | MR | Zbl

[MAG] The Magma Computational Algebra System for Algebra, Number Theory and Geometry. available via the magma home page http://wvw. maths. usyd. edu. au:8000/u/magma/.

[Mar] J. Martinet, Les Réseaux parfaits des espaces Euclidiens. Masson (1996). | MR | Zbl

[Marl] J. Martinet, Sur certains designs sphériques liés à des réseaux entiers. In [EM].

[MiH] J. Milnor, D. Husemoller, Symmetric bilinear forms. Springer-Verlag (1973). | MR | Zbl

[Scha] W. Scharlau, Quadratic and Hermitian Forms. Springer Grundlehren 270 (1985). | MR | Zbl

[Sou] B. Souvignier, Irreducible finite integral matrix groups of degree 8 and 10. Math. Comp. 61 207 (1994), 335-350. | MR | Zbl

[Ven] B. Venkov, Réseaux et designs sphériques. Notes taken by J. Martinet of lectures by B. Venkov at Bordeaux (1996/1997). In [EM].