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arXiv · 0807.2620

Newton polygons of higher order in algebraic number theory

Jordi Guardia·Jesus Montes·Enric Nart
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Abstract

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 Ø. Ore. As an application, we obtain fast algorithms to compute discriminants, prime ideal decomposition and integral bases of number fields.

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Jordi Guardia, Jesus Montes, Enric Nart. 2008-10-31. Newton polygons of higher order in algebraic number theory. https://arxiv.org/abs/0807.2620

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