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Minkowski-Hlawka Theorem

There exist lattices in n dimensions having hypersphere packing densities satisfying

eta>=(zeta(n))/(2^(n-1)),

where zeta(n) is the Riemann zeta function. However, the proof of this theorem is nonconstructive and it is still not known how to actually construct packings that are this dense.

See also

Hermite Constants, Hypersphere Packing

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References

Conway, J. H. and Sloane, N. J. A. Sphere Packings, Lattices, and Groups, 2nd ed. New York: Springer-Verlag, pp. 14-16, 1993.Pach, J. and Agarwal, P. K. Combinatorial Geometry. New York: Wiley, 1995.

Referenced on Wolfram|Alpha

Minkowski-Hlawka Theorem

Cite this as:

Weisstein, Eric W. "Minkowski-Hlawka Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Minkowski-HlawkaTheorem.html

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