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A p-adic approach to solutions of a polynomial congruence modulo pα
Published online by Cambridge University Press: 26 February 2010
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Let where a0≠0, m≥2, n = e1 + … + em and the ξi(1≤i≤m) are the distinct zeros of f in some algebraic closure of the p-adic field . Then K = (ξ1, ξ2, …, ξm) is a finite separable extension of and we denote by “ord” the unique extension of the (additive) p-adic valuation on to K, normalized with ord p = 1.
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