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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Primitive free cubics with specified norm and trace


Authors: Sophie Huczynska and Stephen D. Cohen
Journal: Trans. Amer. Math. Soc. 355 (2003), 3099-3116
MSC (2000): Primary 11T06; Secondary 11A25, 11T24, 11T30
Published electronically: April 25, 2003
MathSciNet review: 1974677
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Abstract: The existence of a primitive free (normal) cubic $x^3-ax^2+cx-b$ over a finite field $F$ with arbitrary specified values of $a$ ($\neq 0$) and $b$ (primitive) is guaranteed. This is the most delicate case of a general existence theorem whose proof is thereby completed.


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Additional Information

Sophie Huczynska
Affiliation: Department of Mathematics, University of Glasgow, Glasgow G12 8QW, Scotland
Address at time of publication: School of Informatics, University of Edinburgh, Edinburgh EH8 9LE, Scotland
Email: shuczyns@inf.ed.ac.uk

Stephen D. Cohen
Affiliation: Department of Mathematics, University of Glasgow, Glasgow G12 8QW, Scotland
Email: sdc@maths.gla.ac.uk

DOI: http://dx.doi.org/10.1090/S0002-9947-03-03301-4
PII: S 0002-9947(03)03301-4
Received by editor(s): September 26, 2002
Received by editor(s) in revised form: January 30, 2003
Published electronically: April 25, 2003
Article copyright: © Copyright 2003 American Mathematical Society