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On the computation of all extensions of a  -adic field of a given degree
Author(s):
Sebastian
Pauli;
Xavier-François
Roblot.
Journal:
Math. Comp.
70
(2001),
1641-1659.
MSC (2000):
Primary 11S15, 11S05;
Secondary 11Y40
Posted:
March 8, 2001
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Abstract:
Let  be a  -adic field. It is well-known that  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  of a given degree and discriminant.
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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
DOI:
10.1090/S0025-5718-01-01306-0
PII:
S 0025-5718(01)01306-0
Keywords:
$p$-adic fields,
wildly ramified extensions,
Eisenstein polynomials
Received by editor(s):
May 24, 1999
Received by editor(s) in revised form:
January 14, 2000
Posted:
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 of article:
Copyright
2001,
American Mathematical Society
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