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.
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Hoffmann, D.W. The Newton polygon of a product of power series. Manuscripta Math 85, 109–118 (1994). https://doi.org/10.1007/BF02568188
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DOI: https://doi.org/10.1007/BF02568188