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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

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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Additional Information

DOI: http://dx.doi.org/10.1090/S0025-5718-1987-0906194-5
PII: S 0025-5718(1987)0906194-5
Keywords: Imaginary cyclic quartic fields, class number, discriminant
Article copyright: © Copyright 1987 American Mathematical Society