Remote Access Mathematics of Computation
Green Open Access

Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)

Request Permissions   Purchase Content 
 

 

Distinct unit generated totally complex quartic fields


Authors: Lajos Hajdu and Volker Ziegler
Journal: Math. Comp. 83 (2014), 1495-1512
MSC (2010): Primary 11R16, 11R27, 11D85
DOI: https://doi.org/10.1090/S0025-5718-2013-02751-2
Published electronically: July 30, 2013
MathSciNet review: 3167469
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: The problem of characterization of rings whose elements can be expressed as sums of their units has a long history and is also of current interest. In this paper we take up the question of describing totally complex quartic number fields $ K$ with the property that every algebraic integer in $ K$ is the sum of distinct units of $ K$. In particular, we give a short list containing all such fields.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Mathematics of Computation with MSC (2010): 11R16, 11R27, 11D85

Retrieve articles in all journals with MSC (2010): 11R16, 11R27, 11D85


Additional Information

Lajos Hajdu
Affiliation: University of Debrecen, Institute of Mathematics H-4010 Debrecen, P.O. Box 12. Hungary
Email: hajdul@science.unideb.hu

Volker Ziegler
Affiliation: Institute for Analysis and Computational Number Theory, Graz University of Technology Steyrergasse 30/IV, A-8010 Graz, Austria
Email: ziegler@finanz.math.tugraz.at

DOI: https://doi.org/10.1090/S0025-5718-2013-02751-2
Keywords: Unit sum number, additive unit structure, digit expansions
Received by editor(s): May 24, 2012
Received by editor(s) in revised form: August 30, 2012
Published electronically: July 30, 2013
Additional Notes: The first author’s research was supported in part by the OTKA grants K75566, K100339, NK101680, and by the TÁMOP 4.2.1./B-09/1/KONV-2010-0007 project. The project is implemented through the New Hungary Development Plan, cofinanced by the European Social Fund and the European Regional Development Fund.
The second author’s research was supported by the Austrian Science Found (FWF) under the project J2886-NT
Article copyright: © Copyright 2013 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.