Fundamentality of a cubic unit for

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

DOI:
https://doi.org/10.1090/S0025-5718-2010-02383-X

Published electronically:
July 29, 2010

Corrigendum:
Math. Comp. 81 (2012), 2383--2387

MathSciNet review:
2728994

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Abstract | References | Similar Articles | Additional Information

Abstract: Consider a cubic unit of positive discriminant. We present a computational proof of the fact that is a fundamental unit of the order in most cases and determine the exceptions. This extends a similar (but restrictive) result due to E. Thomas.

**1.**H. Cohen,*A Course in Computational Algebraic Number Theory,*Graduate Texts in Mathematics 138, Springer-Verlag (2000). MR**1228206 (94i:11105)****2.**S. Louboutin,*The class-number one problem for some real cubic number fields with negative discriminants,*J. Number Theory 121 (2006), 30-39. MR**2268753 (2007k:11189)****3.**S. Louboutin,*The fundamental unit of some quadratic, cubic or quartic orders,*J. Ramanujan Math. Soc. 23, No.2 (2008), 191-210. MR**2432797 (2009h:11175)****4.**S. Louboutin,*On some cubic or quartic algebraic units,*J. Number Theory, to appear.**5.**T. Nagell,*Zur Theorie der kubishen Irrationalitaten,*Acta Math. 55 (1930), 33-65. MR**1555314****6.**S.-M. Park and G.-N. Lee,*The class number one problem for some totally complex quartic number fields,*J. Number Theory 129 (2009), 1138-1349. MR**2521477****7.**E. Thomas,*Fundamental units for orders in certain cubic number fields*, J. Reine Angew. Math. 310 (1979), 33-55. MR**546663 (81b:12009)**

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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:
https://doi.org/10.1090/S0025-5718-2010-02383-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.