Newton polygons of higher order in algebraic number theory

Details Newton polygons of higher order in algebraic number theory Newton polygons of higher order in algebraic number theory

2008-07-16

arxiv.org/abs/0807.2620v2

Mathematics

Number Theory

In this version we correct some minor mistakes

Scientific paper

We develop a theory of arithmetic Newton polygons of higher order, that provides the factorization of a separable polynomial over a $p$-adic field, together with relevant arithmetic information about the fields generated by the irreducible factors. This carries out a program suggested by \O{}. Ore. As an application, we obtain fast algorithms to compute discriminants, prime ideal decomposition and integral bases of number fields.

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