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The Discriminant of a Dihedral Quintic Field Defined by a Trinomial X 5 + aX + b

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

Abstract

Let ${{X}^{5}}\,+\,aX\,+\,b\,\in \,Z\left[ X \right]$ have Galois group ${{D}_{5}}$ . Let $\theta $ be a root of ${{X}^{5}}\,+\,aX\,+\,b$ . An explicit formula is given for the discriminant of $Q\left( \theta \right)$ .

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References

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[1] Liu, D., Dihedral polynomial congruences and binary quadratic forms: a class field theory approach. Ph.D. thesis, Carleton University, Ottawa, Ontario, Canada, 1992.
[2] Llorente, P., Nart, E. and Vila, N., Discriminants of number fields defined by trinomials. Acta Arith. 43 (1984), 367373.
[3] Marcus, D. A., Number Fields. Springer-Verlag, New York-Heidelberg-Berlin, 1977.
[4] Roland, G., Yui, N. and Zagier, D., A parametric family of quintic polynomials with Galois group D5. J. Number Theory 15 (1982), 137142.
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The Discriminant of a Dihedral Quintic Field Defined by a Trinomial X 5 + aX + b

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

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