Hostname: page-component-848d4c4894-4hhp2 Total loading time: 0 Render date: 2024-05-19T09:09:10.092Z Has data issue: false hasContentIssue false
  • English
  • Français

An application of Siegel's formula over quaternion orders

Published online by Cambridge University Press:  26 February 2010

H.-G. Quebbemann
H.-G. Quebbemann
Affiliation:
Mathematisches Institut der Universität, Einsteinstrasse 62, D-4400 Münster, West Germany.
Get access

Extract

Let Φ : L → ℤ be a positive definite even unimodular quadratic form, L ≅ ℤn; we put f(x) = Φ(x)/2 and call (L, f) a lattice, for short. Let min f be the minimum of the numbers f(x) ≠ 0. Fixing n (a multiple of 8), one is interested in the largest possible minimum. It follows from the theory of modular forms (cf. Sloane [6]) that

Type
Research Article
Information
Mathematika , Volume 31 , Issue 1 , June 1984 , pp. 12 - 16
Copyright
Copyright © University College London 1984

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1.Eichler, M.. Quadratischc Formen und orthogonale Gruppen (Springer-Verlag, 1952).CrossRefGoogle Scholar
2.Kneser, M.. Klassenzahlen definiter quadratischer Formen. Arch. Math., 8 (1957), 241–250.CrossRefGoogle Scholar
3.MacWilliams, F. J., Odlyzko, A. M., Sloane, N. J. A. and Ward, H. N.. Self-dual codes over GF(4). J. Combinatorial Theory, Ser. A, 25 (1978), 288–318.CrossRefGoogle Scholar
4.Milnor, J. and Husemoller, D.. Symmetric bilinear forms (Springer-Verlag, 1973).CrossRefGoogle Scholar
5.Serre, J.-P.. A course in arithmetic (Springer-Verlag, 1973).CrossRefGoogle Scholar
6.Sloane, N. J. A.. Binary codes, lattices and sphere-packings. Combinatorial Surveys: Proc. Sixth British Combinatorial Conf. (Academic Press, 1977), 117–164.Google Scholar
7.Tits, J.. Four presentations of Leech's lattice. Finite simple groups II (Academic Press, 1980), 303–307.Google Scholar
8.Vigneras, M.-F.. Arithmétique des algèbres de quaternions. Springer Lecture Notes, 800 (Springer-Verlag, 1980).CrossRefGoogle Scholar
9.Weil, A.. Sur la formule de Siegel dans la theorie des groupes classiques. Ada Math., 113 (1965), 1–87.Google Scholar