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Cyclic Cubic Fields of Given Conductor and Given Index

Published online by Cambridge University Press:  20 November 2018

Alan K. Silvester
Affiliation:
Department of Mathematics and Statistics, Okanagan University College, Kelowna, BC, V1V 1V7 e-mail: [email protected] e-mail: [email protected]
Blair K. Spearman
Affiliation:
Department of Mathematics and Statistics, Okanagan University College, Kelowna, BC, V1V 1V7 e-mail: [email protected] e-mail: [email protected]
Kenneth S. Williams
Affiliation:
School of Mathematics and Statistics, Carleton University, Ottawa, ON, K1S 5B6 e-mail: [email protected]
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Abstract

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The number of cyclic cubic fields with a given conductor and a given index is determined.

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 2006

References

[1] Berndt, B. C., Evans, R. J. and Williams, K. S., Gauss and Jacobi Sums. Wiley, New York, 1998.Google Scholar
[2] Buell, D. A., Binary Quadratic Forms. Classical Theory and Modern Computations. Springer-Verlag, New York, 1989.Google Scholar
[3] Cohen, H., A Course in Computational Algebraic Number Theory. Graduate Texts in Mathematics 138, Springer-Verlag, Berlin, 1993.Google Scholar
[4] Dickson, L. E., Introduction to the Theory of Numbers. Dover, New York, 1957.Google Scholar
[5] Engstrom, H. T., On the common index divisors of an algebraic field. Trans. Amer. Math. Soc. 32(1930), no. 2, 223237.Google Scholar
[6] Kaplan, P. and Williams, K. S., On a formula of Dirichlet. Far East J. Math. Sci. 5(1997), no. 1, 153157.Google Scholar
[7] Llorente, P. and Nart, E., Effective determination of the decomposition of the rational primes in a cubic field. Proc. Amer. Math. Soc. 87(1983), no. 4, 579585.Google Scholar
[8] Mayer, D. C.,Multiplicities of dihedral discriminants. Math. Comp. 58(1992), 831847.Google Scholar
[9] Muzaffar, H. and Williams, K. S., Evaluation of Weber's functions at quadratic irrationalities. JP J. Algebra Number Theory Appl. 4(2004), no. 2, 209259.Google Scholar
[10] Narkiewicz, W., Elementary and Analytic Theory of Algebraic Numbers. Second edition. Springer-Verlag, Berlin, 1990.Google Scholar