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Mathematics of Computation

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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
MathSciNet review: 906194
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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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Keywords: Imaginary cyclic quartic fields, class number, discriminant
Article copyright: © Copyright 1987 American Mathematical Society