Proceedings of the Japan Academy, Series A, Mathematical Sciences

The proportion of cyclic quartic fields with discriminant divisible by a given prime

Blair K. Spearman and Kenneth S. Williams

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Abstract

An asymptotic formula is given for the number of cyclic quartic fields with discriminant $\leq x$ and divisible by a given prime.

Article information

Source
Proc. Japan Acad. Ser. A Math. Sci., Volume 80, Number 7 (2004), 141-145.

Dates
First available in Project Euclid: 18 May 2005

Permanent link to this document
https://projecteuclid.org/euclid.pja/1116442332

Digital Object Identifier
doi:10.3792/pjaa.80.141

Mathematical Reviews number (MathSciNet)
MR2094536

Zentralblatt MATH identifier
1068.11069

Subjects
Primary: 11R16: Cubic and quartic extensions
Secondary: 11R21: Other number fields 11R29: Class numbers, class groups, discriminants

Keywords
Discriminant cyclic quartic field

Citation

Spearman, Blair K.; Williams, Kenneth S. The proportion of cyclic quartic fields with discriminant divisible by a given prime. Proc. Japan Acad. Ser. A Math. Sci. 80 (2004), no. 7, 141--145. doi:10.3792/pjaa.80.141. https://projecteuclid.org/euclid.pja/1116442332


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References

  • Ou, Z. M., and Williams, K. S.: On the density of cyclic quartic fields. Canad. Math. Bull., 44, 97–104 (2001).
  • Spearman, B. K., and Williams, K. S.: Integers which are discriminants of bicyclic or cyclic quartic fields. JP J. Algebra Number Theory Appl., 1, 179–194 (2001).