A new inequality for the Hermite constants

Roland Bacher (1)

1 IF - Institut Fourier

We prove an inequality of the form $\gamma_n\geq C_n(\gamma_{n-1})$ giving a lower bound for the Hermite constant $\gamma_n$ in dimension $n$ in terms of $\gamma_{n-1}$. Iterating this inequality yields a new proof of the Minkowski-Hlawka bound.

Mots clés: Lattice packing; Hermite constant

Domaines: Théorie des nombres [math.NT]

Roland Bacher. A new inequality for the Hermite constants. International Journal of Number Theory, 2008, 4 (3), pp.363-386. ⟨hal-00021286v2⟩