Newton Polyhedra and p-Adic Estimates of Zeros of Polynomials in np[x, y]
Mohd Atan, Kamel Ariffin (1986) Newton Polyhedra and p-Adic Estimates of Zeros of Polynomials in np[x, y]. Pertanika, 9 (1). pp. 51-56.
Newton polyhedron associated with a polynomial in n pix, is introduced. Existence of a relationship between a Newton polyhedron and zeros of its associated polynomial is proved. This relationship is used to arrive at the p-adic estimates of the zeros. An upper bound to the p-adic orders of these zeros is found using the Newton polyhedron method.
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