St. Petersburg Mathematical Journal

			Journals Home Search Author Info Subscribe Tech Support My Subscriptions Help
ISSN 1547-7371(e) ISSN 1061-0022(p)

Previous issue \| Table of contents \| Next issue Recently posted articles \| Most recent issue \| All issues Previous Article \| Next Article

On integral lattices having an odd minimum

Author(s): J. Martinet; B. Venkov
Original publication: Algebra i Analiz, tom 16 (2004), vypusk 3.
Journal: St. Petersburg Math. J. 16 (2005), 507-539.
MSC (2000): Primary 11H06, 11H50
Posted: May 2, 2005
MathSciNet review: 2083567
Retrieve article in: PDF
This article is available free of charge

Abstract | References | Similar articles | Additional information

Abstract: The kissing number of integral lattices of odd minimum is studied, with special emphasis on the case of minimum .

References:

[B-G]: C. Bachoc and Ph. Gaborit, Designs and self-dual codes with long shadows, J. Combin. Theory Ser. A 105 (2004), 15-34. MR 2030137
[Bt]: C. Batut, Classification of quintic eutactic forms, Math. Comp. 70 (2001), 395-417. MR 1803130 (2001k:11124)
[Bt-M]: C. Batut and J. Martinet, A catalogue of perfect lattices, http://www.math.u-bordeaux.fr/~martinet
[Be]: A.-M. Bergé, On certain Coxeter lattices without perfect sections, J. Algebraic Combin. (to appear).
[PARI]: H. Cohn et al., User's guide to PARI, http://www.parigp-home.de.
[C-E]: H. Cohn and N. Elkies, New upper bounds on sphere packings. I, Ann. of Math. (2) 157 (2003), 689-714. MR 1973059 (2004b:11096)
[C-S]: J. H. Conway and N. J. A. Sloane, Sphere packings, lattices and groups, Grundlehren Math. Wiss., vol. 290, Springer-Verlag, New York, 1988; 2nd ed., 1993; 3rd ed., 1999. MR 1194619 (93h:11069); MR 1662447 (2002b:11077)
[C-S1]: -, Low-dimensional lattices. V. Integral coordinates for integral lattices, Proc. Roy. Soc. London Ser. A 426 (1989), 211-232. MR 1030461 (90m:11100)
[C-S2]: -, On lattices equivalent to their duals, J. Number Theory 48 (1994), 373-382. MR 1293868 (95j:11063)
[J]: D. O. Jaquet, Énumération complète des classes de formes parfaites en dimension , Thèse, Neuchâtel, 1991.
[M]: J. Martinet, Perfect lattices in Euclidean spaces, Grundlehren Math. Wiss., vol. 327, Springer-Verlag, Berlin, 2003 (updated English version of ``Les réseaux parfaits des espaces euclidiens'', Masson, Paris, 1996). MR 1957723 (2003m:11099)
[M1]: -, Sur l'indice d'un sous-réseau (with an appendix by C. Batut), Réseaux Euclidiens, Designs Sphériques et Formes Modulaires, Monogr. Enseign. Math., vol. 37, Enseign. Math., Gèneve, 2001, pp. 163-211. MR 1878750 (2002k:11109)
[N-V]: G. Nebe and B. Venkov, The strongly perfect lattices in dimension , J. Théor. Nombres Bordeaux 12 (2000), 503-518. MR 1823200 (2002f:11081)
[Neu]: A. Neumaier, On norm three vectors in integral Euclidean lattices. I, Math. Z. 183 (1983), 565-574. MR 0710772 (85d:11064)
[Pl-P]: W. Plesken and M. Pohst, Constructing integral lattices with prescribed minimum. I, Math. Comp. 45 (1985), 209-221, S5-S16. MR 0790654 (87e:11077)
[S-Y]: E. Shult and A. Yanushka, Near -gons and line systems, Geom. Dedicata 9 (1980), 1-72. MR 0566437 (82b:51018)
[V]: B. B. Venkov, Réseaux et designs sphériques, Réseaux Euclidiens, Designs Sphériques et Formes Modulaires, Monogr. Enseign. Math., vol. 37, Enseign. Math., Gèneve, 2001, pp. 10-86. MR 1878745 (2002m:11061)
[W1]: G. L. Watson, On the minimum points of a positive quadratic form, Mathematika 18 (1971), 60-70. MR 0289421 (44:6612)
[W2]: -, The number of minimum points of a positive quadratic form having no perfect binary section with the same minimum, Proc. London Math. Soc. (3) 24 (1972), 625-646. MR 0308051 (46:7166)

	Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
\|