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Calculation of the class numbers of imaginary cyclic quartic fields


Authors: Kenneth Hardy, R. H. Hudson, D. Richman, Kenneth S. Williams and N. M. Holtz
Journal: Math. Comp. 49 (1987), 615-620
MSC: Primary 11Y40; Secondary 11R16, 11R29
DOI: https://doi.org/10.1090/S0025-5718-1987-0906194-5
MathSciNet review: 906194
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Abstract | References | Similar Articles | Additional Information

Abstract: Any imaginary cyclic quartic field can be expressed uniquely in the form $ K = Q(\sqrt {A(D + B\sqrt D )} )$, where A is squarefree, odd and negative, $ D = {B^2} + {C^2}$ is squarefree, $ B > 0,C > 0$, and $ (A,D) = 1$. Explicit formulae for the discriminant and conductor of K are given in terms of A, B, C, D. The calculation of tables of the class numbers $ h(K)$ of such fields K is described.


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

  • [1] E. D. Bolker, Elementary Number Theory, Benjamin, New York, 1970. MR 0252310 (40:5531)
  • [2] Harvey Cohn, "A computation of some bi-quadratic class numbers," MTAC, v. 12, 1958, pp. 213-217. MR 0100972 (20:7397)
  • [3] M.-N. Gras, Table Numérique du Nombre de Classes et des Unités des Extensions Cycliques Réelles de Degré 4 de Q, Publ. Math. Univ. Besançon, 1977/78, fasc. 2, 53 pp.
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Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1987-0906194-5
Keywords: Imaginary cyclic quartic fields, class number, discriminant
Article copyright: © Copyright 1987 American Mathematical Society

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