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

 

Improvement of Nakamula's upper bound for the absolute discriminant of a sextic number field with two real conjugates


Author: R. J. Stroeker
Journal: Math. Comp. 59 (1992), 203-211
MSC: Primary 11R27; Secondary 11R21, 11R29
MathSciNet review: 1134739
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Abstract: Let K be the compositum of a real quadratic number field $ {{\mathbf{K}}_2}$ and a complex cubic number field $ {{\mathbf{K}}_3}$. Further, let $ \varepsilon $ be a unit of K which is also a relative unit with respect to $ {\mathbf{K}}/{{\mathbf{K}}_2}$ and $ {\mathbf{K}}/{{\mathbf{K}}_3}$. The absolute discriminant of this non-Galois sextic number field K is estimated from above by a simple, strictly increasing, polynomial function of $ \varepsilon $. This estimate, which can be used to determine a generator for the cyclic group of relative units, substantially improves a similar bound due to Nakamula. The method employed makes nontrivial use of computer algebra techniques.


References [Enhancements On Off] (What's this?)

  • [1] Macintosh Maple 4.2.1, Symbolic Computation Group, Department of Computer Science, Univ. of Waterloo, 1990.
  • [2] Ken Nakamula, Class number calculation of a sextic field from the elliptic unit, Acta Arith. 45 (1985), no. 3, 229–247. MR 808023 (87a:11113)
  • [3] R. J. Stroeker, Appendix to improvement of Nakamula's upper bound for the absolute discriminant of a sextic number field with two real conjugates, Econometric Inst., Erasmus Univ. Rotterdam, Report Series 9069/B, 1990.

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Additional Information

DOI: http://dx.doi.org/10.1090/S0025-5718-1992-1134739-3
PII: S 0025-5718(1992)1134739-3
Article copyright: © Copyright 1992 American Mathematical Society