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The Discriminant of a Dihedral Quintic Field Defined by a Trinomial X5 + aX + b

Published online by Cambridge University Press:  20 November 2018

Blair K. Spearman
Affiliation:
Department of Mathematics and Statistics, Okanagan University College, Kelowna, BC, V1V 1V7, email: [email protected]
Kenneth S. Williams
Affiliation:
Centre for Research in Algebra and Number Theory, School of Mathematics and Statistics, Carleton University, Ottawa, Ontario, K1S 5B6, email: [email protected]
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Abstract

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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 $Q\left( \theta \right)$.

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 2002

References

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