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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

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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.
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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