Hostname: page-component-586b7cd67f-tf8b9 Total loading time: 0 Render date: 2024-11-23T21:18:32.021Z Has data issue: false hasContentIssue false

The height of the Leech lattice

Published online by Cambridge University Press:  17 April 2009

Kok Seng Chua
Affiliation:
Institute of High Performance Computing, 89C Science Park Drive, #02–11/12 The Rutherfold, Singapore 118261, e-mail: [email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We derive explicit formulae for the height of the Leech lattice and give evidence supporting the conjecture that the Leech lattice has minimum height and minimum values of the Epstein zeta function among all 24 dimensional lattices of determinant one.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 2000

References

[1]Chiu, P., ‘Height of flat tori’, Proc. Amer. Math. Soc. 125 (1997), 723730.CrossRefGoogle Scholar
[2]Conway, J. and Sloane, J., Sphere packings lattices and groups, (second edition) (Springer-Verlag, Berlin, Heidelberg, New York, 1988).CrossRefGoogle Scholar
[3]Hecke, E., ‘Lectures on Dirichlet series, modular functions and quadratic forms’, (1983).Google Scholar
[4]Montgomery, H., ‘Minimal theta functions’, Glasgow Math. J. 30 (1988), 7585.CrossRefGoogle Scholar
[5]Osgood, B., Phillips, R. and Sarnak, P., ‘Extremals of determinants of Laplacians’, J. Funct. Anal. 80 (1988), 148211.CrossRefGoogle Scholar
[6]Ryshkov, S., ‘On the equation of final ζ-optimality of lattices providing the densest lattice packing of n-dimensional sphere’, (English translation), Siberian Math. J. 14 (1973), 743750.CrossRefGoogle Scholar
[7]Terras, A., ‘The minimum of quadratic form and the behaviour of Epstein and Dedekind zeta functions’, J. Number Theory 12 (1980), 258272.CrossRefGoogle Scholar