  This paper deals with Arakelov vector bundles over an arithmetic curve, i.e.
over the set of places of a number field. The main result is that for each
semistable bundle E, there is a bundle F such that $E \otimes F$ has at least a
certain slope, but no global sections. It is motivated by an analogous theorem
of Faltings for vector bundles over algebraic curves and contains the
Minkowski-Hlawka theorem on sphere packings as a special case. The proof uses
an adelic version of Siegel's mean value formula.
