Newton polygons of higher order in algebraic number theory

Jordi Guàrdia, Jesús Montes, Enric Nart

Research output: Contribution to journalArticleResearchpeer-review

32 Citations (Scopus)

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. © 2011 American Mathematical Society.
Original languageEnglish
Pages (from-to)361-416
JournalTransactions of the American Mathematical Society
Volume364
Issue number1
DOIs
Publication statusPublished - 1 Jan 2012

Keywords

  • Discriminant
  • Integral basis
  • Local field
  • Newton polygon
  • Number field
  • P-adic factorization
  • Prime ideal decomposition

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