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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

Fundamentality of a cubic unit $ u$ for $ \mathbb{Z}[u]$


Authors: J. Beers, D. Henshaw, C. K. McCall, S. B. Mulay and M. Spindler
Journal: Math. Comp. 80 (2011), 563-578
MSC (2010): Primary 11R16; Secondary 11R27
Published electronically: July 29, 2010
Corrigendum: Math. Comp. 81 (2012), 2383--2387
MathSciNet review: 2728994
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Abstract: Consider a cubic unit $ u$ of positive discriminant. We present a computational proof of the fact that $ u$ is a fundamental unit of the order $ \mathbb{Z}[u]$ in most cases and determine the exceptions. This extends a similar (but restrictive) result due to E. Thomas.


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Additional Information

J. Beers
Affiliation: The College of New Jersey, Ewing, New Jersey 08628
Email: JasonBBeers@gmail.com

D. Henshaw
Affiliation: Department of Mathematical Sciences, Clemson University, Clemson, South Carolina 29634
Email: davidlhenshaw@gmail.com

C. K. McCall
Affiliation: Department of Mathematics, 719 Patterson Office Tower, University of Kentucky, Lexington, Kentucky 40506-0027
Email: cmccall@ms.uky.edu

S. B. Mulay
Affiliation: Department of Mathematics, University of Tennessee, Knoxville, Tennessee 37996-1300
Email: mulay@math.utk.edu

M. Spindler
Affiliation: Department of Mathematics, Johns Hopkins University, Baltimore, Maryland 21218
Email: spindler@math.jhu.edu

DOI: http://dx.doi.org/10.1090/S0025-5718-2010-02383-X
PII: S 0025-5718(2010)02383-X
Keywords: Cubic orders, fundamental units.
Received by editor(s): April 20, 2009
Received by editor(s) in revised form: July 27, 2009, and October 18, 2009
Published electronically: July 29, 2010
Additional Notes: The authors were supported by the NSF REU award no. 0552774, 2008
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.