The Newton polygon of a product of power series
DW Hoffmann - manuscripta mathematica, 1994 - Springer
DW Hoffmann
manuscripta mathematica, 1994•SpringerLet F be a field with a non-trivial valuation υ: F→ ℝ∪{+∞}. To any power series in one
variable over F one can associate a Newton polygon with respect to this valuation. Let N 1
and N 2 be polygons which arise as Newton polygons of power series over F. We determine
the set of polygons N with the property that there exist power series fi with respective Newton
polygon N i, i= 1, 2, such that the product f 1 f 2 has Newton polygon N.
variable over F one can associate a Newton polygon with respect to this valuation. Let N 1
and N 2 be polygons which arise as Newton polygons of power series over F. We determine
the set of polygons N with the property that there exist power series fi with respective Newton
polygon N i, i= 1, 2, such that the product f 1 f 2 has Newton polygon N.
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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