staple
With cedram.org

Search the site

Table of contents for this issue | Previous article | Next article
Scott Duke Kominers; Zachary Abel
Configurations of rank-${40r}$ extremal even unimodular lattices (${r=1,2,3}$)
Journal de théorie des nombres de Bordeaux, 20 no. 2 (2008), p. 365-371, doi: 10.5802/jtnb.632
Article PDF | Reviews MR 2477509 | Zbl pre05543167
Keywords: Even unimodular lattices, extremal lattices, weighted theta series

Résumé - Abstract

We show that if $L$ is an extremal even unimodular lattice of rank $40r$ with $r=1,2,3$, then $L$ is generated by its vectors of norms $4r$ and $4r+2$. Our result is an extension of Ozeki’s result for the case $r=1$.

Bibliography

[1] C. Bachoc, G. Nebe, B. Venkov, Odd unimodular lattices of minimum 4. Acta Arithmetica 101 (2002), 151–158.  MR 1880305 |  Zbl 0998.11034
[2] J. H. Conway, N. J. A. Sloane, Sphere Packing, Lattices and Groups (3rd edition). Springer-Verlag, New York, 1999.  MR 1662447 |  Zbl 0915.52003
[3] W. Ebeling, Lattices and Codes (2nd edition). Vieweg, Germany, 2002.  MR 1938666 |  Zbl 1030.11030
[4] N. D. Elkies, On the quotient of an extremal Type II lattice of rank $40$, $80$, or $120$ by the span of its minimal vectors. Preprint.
[5] S. D. Kominers, Configurations of extremal even unimodular lattices. To appear, Int. J. Num. Thy. (Preprint arXiv:0706.3082, 21 Jun 2007.) arXiv
[6] M. Ozeki, On even unimodular positive definite quadratic lattices of rank $32$. Math. Z. 191 (1986), 283–291. Article |  MR 818672 |  Zbl 0564.10016
[7] M. Ozeki, On the structure of even unimodular extremal lattices of rank $40$. Rocky Mtn. J. Math. 19 (1989), 847–862.  MR 1043254 |  Zbl 0706.11018
[8] M. Ozeki, On the configurations of even unimodular lattices of rank $48$. Arch. Math. 46 (1986), 247–287.  MR 829816 |  Zbl 0571.10020
[9] J.-P. Serre, A Course in Arithmetic. Springer-Verlag, New York, 1973.  MR 344216 |  Zbl 0256.12001