The Newton polygon of a product of power series

Summary LetF be a field with a non-trivial valuation υ:F→ℝ∪{+∞}. To any power series in one variable overF one can associate a Newton polygon with respect to this valuation. LetN ₁ andN ₂ be polygons which arise as Newton polygons of power series overF. We determine the set of polygonsN with the property that there exist power seriesf _i with respective Newton polygonN _i ,i=1,2, such that the productf ₁ f ₂ has Newton polygonN. Supported by a grant from the DFG This article was processed by the author using the LATEX style filepljour1 from Springer-Verlag.