Newton polygons of higher order in algebraic number theory
Number Theory
2008-10-31 v2
Abstract
We develop a theory of arithmetic Newton polygons of higher order, that provides the factorization of a separable polynomial over a -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.
Keywords
Cite
@article{arxiv.0807.2620,
title = {Newton polygons of higher order in algebraic number theory},
author = {Jordi Guardia and Jesus Montes and Enric Nart},
journal= {arXiv preprint arXiv:0807.2620},
year = {2008}
}
Comments
In this version we correct some minor mistakes