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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2024 MCQ for Mathematics of Computation is 1.78.

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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

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.
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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: https://doi.org/10.1090/S0025-5718-1987-0906194-5
  • MathSciNet review: 906194