Hostname: page-component-cd9895bd7-dzt6s Total loading time: 0 Render date: 2024-12-30T19:25:50.406Z Has data issue: false hasContentIssue false
  • English
  • Français

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: [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]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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

[1] Liu, D., Dihedral polynomial congruences and binary quadratic forms: a class field theory approach. Ph.D. thesis, Carleton University, Ottawa, Ontario, Canada, 1992.Google Scholar
[2] Llorente, P., Nart, E. and Vila, N., Discriminants of number fields defined by trinomials. Acta Arith. 43 (1984), 367–373.Google Scholar
[3] Marcus, D. A., Number Fields. Springer-Verlag, New York-Heidelberg-Berlin, 1977.Google Scholar
[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