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A NEW INEQUALITY FOR THE HERMITE CONSTANTS
International Journal of Number Theory
We describe continuous increasing functions C n (x) such that γ n ≥ C n (γ n−1 ) where γ m is Hermite's constant in dimension m. This inequality yields a new proof of the Minkowski-Hlawka bound ∆ n ≥ ζ(n)2 1−n for the maximal density ∆ n of n−dimensional lattice-packings. 1doi:10.1142/s1793042108001390 fatcat:tirmm7f24nejtfsmgxmmiwx33y