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Cyclic Cubic Fields of Given Conductor and Given Index

  • Alan K. Silvester (a1), Blair K. Spearman (a1) and Kenneth S. Williams (a2)

Abstract

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

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Copyright

References

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[1] Berndt, B. C., Evans, R. J. and Williams, K. S., Gauss and Jacobi Sums. Wiley, New York, 1998.
[2] Buell, D. A., Binary Quadratic Forms. Classical Theory and Modern Computations. Springer-Verlag, New York, 1989.
[3] Cohen, H., A Course in Computational Algebraic Number Theory. Graduate Texts in Mathematics 138, Springer-Verlag, Berlin, 1993.
[4] Dickson, L. E., Introduction to the Theory of Numbers. Dover, New York, 1957.
[5] Engstrom, H. T., On the common index divisors of an algebraic field. Trans. Amer. Math. Soc. 32(1930), no. 2, 223237.
[6] Kaplan, P. and Williams, K. S., On a formula of Dirichlet. Far East J. Math. Sci. 5(1997), no. 1, 153157.
[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.
[8] Mayer, D. C.,Multiplicities of dihedral discriminants. Math. Comp. 58(1992), 831847.
[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.
[10] Narkiewicz, W., Elementary and Analytic Theory of Algebraic Numbers. Second edition. Springer-Verlag, Berlin, 1990.
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Cyclic Cubic Fields of Given Conductor and Given Index

  • Alan K. Silvester (a1), Blair K. Spearman (a1) and Kenneth S. Williams (a2)

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