The strongly perfect lattices of dimension 10

Gabriele Nebe; Boris Venkov

Journal de théorie des nombres de Bordeaux (2000)

  • Volume: 12, Issue: 2, page 503-518
  • ISSN: 1246-7405

Abstract

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

How to cite

top

Nebe, Gabriele, and Venkov, Boris. "The strongly perfect lattices of dimension $10$." Journal de théorie des nombres de Bordeaux 12.2 (2000): 503-518. <http://eudml.org/doc/248503>.

@article{Nebe2000,
abstract = {This paper classifies the strongly perfect lattices in dimension $10$. There are up to similarity two such lattices, $K^\{\prime \}_\{10\}$ and its dual lattice.},
author = {Nebe, Gabriele, Venkov, Boris},
journal = {Journal de théorie des nombres de Bordeaux},
keywords = {perfect lattice; spherical design},
language = {eng},
number = {2},
pages = {503-518},
publisher = {Université Bordeaux I},
title = {The strongly perfect lattices of dimension $10$},
url = {http://eudml.org/doc/248503},
volume = {12},
year = {2000},
}

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
PB - Université Bordeaux I
VL - 12
IS - 2
SP - 503
EP - 518
AB - This paper classifies the strongly perfect lattices in dimension $10$. There are up to similarity two such lattices, $K^{\prime }_{10}$ and its dual lattice.
LA - eng
KW - perfect lattice; spherical design
UR - http://eudml.org/doc/248503
ER -

References

top
  1. [BaV] C. Bachoc, B. Venkov, Modular forms, lattices and spherical designs. In [EM]. Zbl1061.11035
  2. [Cas] J.W.S. Cassels, Rational quadratic forms. Academic Press (1978). Zbl0395.10029MR522835
  3. [CoS] J.H. Conway, N.J A. Sloane, Sphere Packings, Lattices and Groups. 3rd edition, Springer-Verlag (1998). Zbl0915.52003
  4. [CoS] J.H. Conway, N.J.A. Sloane, On Lattices Equivalent to Their Duals. J. Number Theory48 (1994), 373-382. Zbl0810.11041MR1293868
  5. [EM] Réseaux euclidiens, designs sphériques et groupes. Edited by J. Martinet. Enseignement des Mathématiques, monographie 37, to appear. Zbl1054.11034MR1881618
  6. [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/. 
  7. [Mar] J. Martinet, Les Réseaux parfaits des espaces Euclidiens. Masson (1996). Zbl0869.11056MR1434803
  8. [Marl] J. Martinet, Sur certains designs sphériques liés à des réseaux entiers. In [EM]. 
  9. [MiH] J. Milnor, D. Husemoller, Symmetric bilinear forms. Springer-Verlag (1973). Zbl0292.10016MR506372
  10. [Scha] W. Scharlau, Quadratic and Hermitian Forms. Springer Grundlehren270 (1985). Zbl0584.10010MR770063
  11. [Sou] B. Souvignier, Irreducible finite integral matrix groups of degree 8 and 10. Math. Comp.61207 (1994), 335-350. Zbl0830.20074MR1213836
  12. [Ven] B. Venkov, Réseaux et designs sphériques. Notes taken by J. Martinet of lectures by B. Venkov at Bordeaux (1996/1997). In [EM]. 

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.