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On solving relative norm equations in algebraic number fields

Authors:	C Fieker A Jurk M Pohst

Institution:	Fachbereich 3 Mathematik, Sekretariat MA~8--1, Technische Universität Berlin, Straße des 17. Juni 136, D-10623 Berlin, Germany ; Desdorfer Weg 15, 50181 Bedburg, Germany M. Pohst ; Fachbereich 3 Mathematik, Sekretariat MA~8--1, Technische Universität Berlin, Straße des 17. Juni 136, D-10623 Berlin, Germany

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.

Keywords:	Algebraic number theory norm equations relative norm equations relative extensions

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