A NEW INEQUALITY FOR THE HERMITE CONSTANTS

ROLAND BACHER
2008 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. 1
doi:10.1142/s1793042108001390 fatcat:tirmm7f24nejtfsmgxmmiwx33y