English

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 pp-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