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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

On solving relative norm equations
in algebraic number fields


Authors: C. Fieker, A. Jurk and M. Pohst
Journal: Math. Comp. 66 (1997), 399-410
MSC (1991): Primary 11Y40
MathSciNet review: 1355008
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Abstract: Let ${\Bbb Q} \subseteq{\cal E} \subseteq{\cal F} $ be algebraic number fields and $M\subset {\cal F} $ a free $o_{{\cal E} } $-module. We prove a theorem which enables us to determine whether a given relative norm equation of the form $|\mathop {N_{{\cal F} /{\cal E} }^{}}(\eta )| = |\theta |$ has any solutions $\eta \in M$ at all and, if so, to compute a complete set of nonassociate solutions. Finally we formulate an algorithm using this theorem, consider its algebraic complexity and give some examples.


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Additional Information

C. Fieker
Affiliation: Fachbereich 3 Mathematik, Sekretariat MA 8–1, Technische Universität Berlin, Straße des 17. Juni 136, D-10623 Berlin, Germany
Email: fieker@math.tu-berlin.de

A. Jurk
Affiliation: Desdorfer Weg 15, 50181 Bedburg, Germany

M. Pohst
Affiliation: Fachbereich 3 Mathematik, Sekretariat MA 8–1, Technische Universität Berlin, Straße des 17. Juni 136, D-10623 Berlin, Germany
Email: pohst@math.tu-berlin.de

DOI: http://dx.doi.org/10.1090/S0025-5718-97-00761-8
PII: S 0025-5718(97)00761-8
Keywords: Algebraic number theory, norm equations, relative norm equations, relative extensions
Received by editor(s): August 30, 1994
Received by editor(s) in revised form: March 27, 1995, and July 20, 1995
Article copyright: © Copyright 1997 American Mathematical Society