Newton polygons of higher order in algebraic number theory
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- by Jordi Guàrdia, Jesús Montes and Enric Nart PDF
- Trans. Amer. Math. Soc. 364 (2012), 361-416 Request permission
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.References
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Additional Information
- Jordi Guàrdia
- Affiliation: Departament de Matemàtica Aplicada IV, Escola Politècnica Superior d’Enginyera de Vilanova i la Geltrú, Av. Víctor Balaguer s/n. E-08800 Vilanova i la Geltrú, Catalonia, Spain
- MR Author ID: 650818
- Email: guardia@ma4.upc.edu
- Jesús Montes
- Affiliation: Departament de Ciències Econòmiques i Socials, Facultat de Ciències Socials, Universitat Abat Oliba CEU, Bellesguard 30, E-08022 Barcelona, Catalonia, Spain
- Email: montes3@uao.es
- Enric Nart
- Affiliation: Departament de Matemàtiques, Universitat Autònoma de Barcelona, Edifici C, E-08193 Bellaterra, Barcelona, Catalonia, Spain
- Email: nart@mat.uab.cat
- Received by editor(s): October 31, 2008
- Received by editor(s) in revised form: June 15, 2010
- Published electronically: May 18, 2011
- Additional Notes: This work was partially supported by MTM2009-13060-C02-02 and MTM2009-10359 from the Spanish MEC
- © Copyright 2011
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 364 (2012), 361-416
- MSC (2010): Primary 11S15; Secondary 11R04, 11R29, 11Y40
- DOI: https://doi.org/10.1090/S0002-9947-2011-05442-5
- MathSciNet review: 2833586