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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  and
Kenneth S. Williams
Blair K. Spearman
Affiliation:
Department of Mathematics and Statistics, Okanagan University College, Kelowna, BC, V1V 1V7, email: bkspearm@okuc02.okanagan.bc.ca
Kenneth S. Williams
Affiliation:
Centre for Research in Algebra and Number Theory, School of Mathematics and Statistics, Carleton University, Ottawa, Ontario, K1S 5B6, email: williams@math.carleton.ca
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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 $Q\left( \theta \right)$.

Keywords

11R2111R29dihedral quintic fieldtrinomialdiscriminant
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 45 , Issue 1 , 01 March 2002 , pp. 138 - 153
Copyright
Copyright © Canadian Mathematical Society 2002

References

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[4] Roland, G., Yui, N. and Zagier, D., A parametric family of quintic polynomials with Galois group D5. J. Number Theory 15 (1982), 137–142.Google Scholar