Fundamentality of a cubic unit $u$ for $\mathbb {Z}[u]$
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- by J. Beers, D. Henshaw, C. K. McCall, S. B. Mulay and M. Spindler PDF
- Math. Comp. 80 (2011), 563-578 Request permission
Corrigendum: Math. Comp. 81 (2012), 2383-2387.
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.References
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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
- 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
- © Copyright 2010
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Math. Comp. 80 (2011), 563-578
- MSC (2010): Primary 11R16; Secondary 11R27
- DOI: https://doi.org/10.1090/S0025-5718-2010-02383-X
- MathSciNet review: 2728994