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On the Density of Cyclic Quartic Fields

Published online by Cambridge University Press:  20 November 2018

Zhiming M. Ou  and
Kenneth S. Williams
Zhiming M. Ou
Affiliation:
Department of Basic Science Beijing University of Posts and Telecommunications Beijing 100876 People’s Republic of China
Kenneth S. Williams
Affiliation:
Centre for Research in Algebra and Number Theory School of Mathematics and Statistics Carleton University Ottawa, Ontario K1S 5B6, williams@math.carleton.ca
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Abstract

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An asymptotic formula is obtained for the number of cyclic quartic fields over $Q$ with discriminant $\le \,x$.

Keywords

11R1611R29cyclic quartic fieldsdensitydiscriminant
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 44 , Issue 1 , 01 March 2001 , pp. 97 - 104
Copyright
Copyright © Canadian Mathematical Society 2001

References

[1] Baily, A. M., On the density of discriminants of quartic fields. J. Reine Angew Math. 315 (1980), 190–210.Google Scholar
[2] Hardy, K., Hudson, R. H., Richman, D., Williams, K. S. and Holtz, N. M., Calculation of class numbers of imaginary cyclic quartic fields. Carleton-Ottawa Math. Lecture Note Series 7, July 1986.Google Scholar
[3] Hudson, R. H. and Williams, K. S., The integers of a cyclic quartic field. Rocky Mountain J. Math. 20 (1990), 145–150.Google Scholar