On the computation of all extensions of a $p$-adic field of a given degree
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- by Sebastian Pauli and Xavier-François Roblot PDF
- Math. Comp. 70 (2001), 1641-1659 Request permission
Abstract:
Let $\mathbf {k}$ be a $p$-adic field. It is well-known that $\mathbf {k}$ has only finitely many extensions of a given finite degree. Krasner has given formulae for the number of extensions of a given degree and discriminant. Following his work, we present an algorithm for the computation of generating polynomials for all extensions $\mathbf {K}/\mathbf {k}$ of a given degree and discriminant.References
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Additional Information
- Sebastian Pauli
- Affiliation: Centre Interuniversitaire en Calcul Mathématique Algébrique, Concordia University, 1455 de Maisonneuve Blvd. W., Montréal, Québec, H3G 1M8, CANADA
- Email: pauli@cicma.concordia.ca
- Xavier-François Roblot
- Affiliation: Institut Girard Desargues, Université Claude Bernard (Lyon 1), 43, boulevard du 11 Novembre 1918, 69622 Villeurbanne cedex, France
- Email: roblot@desargues.univ-lyon1.fr
- Received by editor(s): May 24, 1999
- Received by editor(s) in revised form: January 14, 2000
- Published electronically: March 8, 2001
- Additional Notes: The work of the first author was supported in part by ISM and FCAR/CICMA (Québec).
The work of the second author was supported in part by NSERC (Canada) and FCAR/CICMA (Québec).
We would like to thank David Ford for his careful reading of the original manuscript and for his useful comments. - © Copyright 2001 American Mathematical Society
- Journal: Math. Comp. 70 (2001), 1641-1659
- MSC (2000): Primary 11S15, 11S05; Secondary 11Y40
- DOI: https://doi.org/10.1090/S0025-5718-01-01306-0
- MathSciNet review: 1836924