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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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Calculation of the class numbers of imaginary cyclic quartic fields
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by Kenneth Hardy, R. H. Hudson, D. Richman, Kenneth S. Williams and N. M. Holtz PDF
Math. Comp. 49 (1987), 615-620 Request permission


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.
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Additional Information
  • © Copyright 1987 American Mathematical Society
  • Journal: Math. Comp. 49 (1987), 615-620
  • MSC: Primary 11Y40; Secondary 11R16, 11R29
  • DOI:
  • MathSciNet review: 906194