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

Published:2002-03-01
Printed: Mar 2002
• Blair K. Spearman
• Kenneth S. Williams
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## Abstract

Let $X^5 + aX + b \in Z[X]$ have Galois group $D_5$. Let $\theta$ be a root of $X^5 + aX + b$. An explicit formula is given for the discriminant of $Q(\theta)$.
 Keywords: dihedral quintic field, trinomial, discriminant
 MSC Classifications: 11R21 - Other number fields 11R29 - Class numbers, class groups, discriminants

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