On solving relative norm equations in algebraic number fields
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- by C. Fieker, A. Jurk and M. Pohst PDF
- Math. Comp. 66 (1997), 399-410 Request permission
Abstract:
Let $\mathbb {Q}\subseteq \mathcal {E}\subseteq \mathcal {F}$ be algebraic number fields and $M\subset \mathcal {F}$ a free $o\varepsilon$-module. We prove a theorem which enables us to determine whether a given relative norm equation of the form $|N_{\mathcal {F}/\mathcal {E}}(\eta )| = |\theta |$ 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.References
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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
- Received by editor(s): August 30, 1994
- Received by editor(s) in revised form: March 27, 1995, and July 20, 1995
- © Copyright 1997 American Mathematical Society
- Journal: Math. Comp. 66 (1997), 399-410
- MSC (1991): Primary 11Y40
- DOI: https://doi.org/10.1090/S0025-5718-97-00761-8
- MathSciNet review: 1355008