2013-05-292013-05-292003Hoffmann, N. (2003), 'Stability of Arakelov Bundles and Tensor Products without Global Sections', Documenta Mathematica, Vol. 8, p115-123.http://www.math.uni-bielefeld.de/documenta/vol-08/07.htmlhttp://hdl.handle.net/10395/1914This 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⊗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.engThis article was originally published in Documenta Mathematica,(2003) Vol. 15 and is available through the following link http://www.math.uni-bielefeld.de/documenta/index.htmlArakelov bundleArtihmetic curveTensor productLattice sphere packingMean value formulaMinkowski-Hlawka theoremArticle