Configurations of rank- extremal even unimodular lattices ()
Scott Duke Kominers[1]; Zachary Abel[2]
- [1] Department of Mathematics Harvard University c/o 8520 Burning Tree Road Bethesda, Maryland, 20817, USA
- [2] Department of Mathematics Harvard University c/o 17134 Earthwind Drive Dallas, Texas, 75248, USA
Journal de Théorie des Nombres de Bordeaux (2008)
- Volume: 20, Issue: 2, page 365-371
- ISSN: 1246-7405
Access Full Article
top
Abstract
topHow to cite
topKominers, Scott Duke, and Abel, Zachary. "Configurations of rank-${40r}$ extremal even unimodular lattices (${r=1,2,3}$)." Journal de Théorie des Nombres de Bordeaux 20.2 (2008): 365-371. <http://eudml.org/doc/10841>.
@article{Kominers2008,
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 $r=1$.},
affiliation = {Department of Mathematics Harvard University c/o 8520 Burning Tree Road Bethesda, Maryland, 20817, USA; Department of Mathematics Harvard University c/o 17134 Earthwind Drive Dallas, Texas, 75248, USA},
author = {Kominers, Scott Duke, Abel, Zachary},
journal = {Journal de Théorie des Nombres de Bordeaux},
keywords = {Even unimodular lattices; extremal lattices; weighted theta series; even unimodular lattices; harmonic theta series; spherical designs},
language = {eng},
number = {2},
pages = {365-371},
publisher = {Université Bordeaux 1},
title = {Configurations of rank-$\{40r\}$ extremal even unimodular lattices ($\{r=1,2,3\}$)},
url = {http://eudml.org/doc/10841},
volume = {20},
year = {2008},
}
TY - JOUR
AU - Kominers, Scott Duke
AU - Abel, Zachary
TI - Configurations of rank-${40r}$ extremal even unimodular lattices (${r=1,2,3}$)
JO - Journal de Théorie des Nombres de Bordeaux
PY - 2008
PB - Université Bordeaux 1
VL - 20
IS - 2
SP - 365
EP - 371
AB - 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 $r=1$.
LA - eng
KW - Even unimodular lattices; extremal lattices; weighted theta series; even unimodular lattices; harmonic theta series; spherical designs
UR - http://eudml.org/doc/10841
ER -
References
top- C. Bachoc, G. Nebe, B. Venkov, Odd unimodular lattices of minimum 4. Acta Arithmetica 101 (2002), 151–158. Zbl0998.11034MR1880305
- J. H. Conway, N. J. A. Sloane, Sphere Packing, Lattices and Groups (3rd edition). Springer-Verlag, New York, 1999. Zbl0915.52003MR1662447
- W. Ebeling, Lattices and Codes (2nd edition). Vieweg, Germany, 2002. Zbl1030.11030MR1938666
- N. D. Elkies, On the quotient of an extremal Type II lattice of rank , , or by the span of its minimal vectors. Preprint.
- S. D. Kominers, Configurations of extremal even unimodular lattices. To appear, Int. J. Num. Thy. (Preprint arXiv:0706.3082, 21 Jun 2007.) Zbl1241.11043
- M. Ozeki, On even unimodular positive definite quadratic lattices of rank . Math. Z. 191 (1986), 283–291. Zbl0564.10016MR818672
- M. Ozeki, On the structure of even unimodular extremal lattices of rank . Rocky Mtn. J. Math. 19 (1989), 847–862. Zbl0706.11018MR1043254
- M. Ozeki, On the configurations of even unimodular lattices of rank . Arch. Math. 46 (1986), 247–287. Zbl0571.10020MR829816
- J.-P. Serre, A Course in Arithmetic. Springer-Verlag, New York, 1973. Zbl0256.12001MR344216
NotesEmbed ?
topYou 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.