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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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Improvement of Nakamula’s upper bound for the absolute discriminant of a sextic number field with two real conjugates
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by R. J. Stroeker PDF
Math. Comp. 59 (1992), 203-211 Request permission


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.
    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 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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Additional Information
  • © Copyright 1992 American Mathematical Society
  • Journal: Math. Comp. 59 (1992), 203-211
  • MSC: Primary 11R27; Secondary 11R21, 11R29
  • DOI:
  • MathSciNet review: 1134739