Okutsu invariants and Newton polygons
Acta Arithmetica(2010)
摘要
Let K be a local field of characteristic zero, O its ring of integers and
F(x) a monic irreducible polynomial with coefficients in O. K. Okutsu attached
to F(x) certain primitive divisor polynomials F_1(x),..., F_r(x), that are
specially close to F(x) with respect to their degree. In this paper we
characterize the Okutsu families [F_1,..., F_r] in terms of certain Newton
polygons of higher order, and we derive some applications: closed formulas for
certain Okutsu invariants, the discovery of new Okutsu invariants, or the
construction of Montes approximations to F(x); these are monic irreducible
polynomials sufficiently close to F(x) to share all its Okutsu invariants. This
perspective widens the scope of applications of Montes' algorithm, which can be
reinterpreted as a tool to compute the Okutsu polynomials and a Montes
approximation, for each irreducible factor of a monic separable polynomial f(x)
in O[x].
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关键词
. local factorization,montes algorithm,newton polygon,okutsu frame.,local field,montes approxima- tion,irreducible polynomial,number theory,algebraic geometry,higher order
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