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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
DOI: https://doi.org/10.1090/S0025-5718-1992-1134739-3
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?)

    Macintosh Maple 4.2.1, Symbolic Computation Group, Department of Computer Science, Univ. of Waterloo, 1990.
  • Ken Nakamula, Class number calculation of a sextic field from the elliptic unit, Acta Arith. 45 (1985), no. 3, 229–247. MR 808023, DOI https://doi.org/10.4064/aa-45-3-229-247
  • 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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Article copyright: © Copyright 1992 American Mathematical Society