Distinct unit generated totally complex quartic fields
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- by Lajos Hajdu and Volker Ziegler PDF
- Math. Comp. 83 (2014), 1495-1512 Request permission
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
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Additional Information
- Lajos Hajdu
- Affiliation: University of Debrecen, Institute of Mathematics H-4010 Debrecen, P.O. Box 12. Hungary
- MR Author ID: 339279
- 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
- MR Author ID: 744740
- Email: ziegler@finanz.math.tugraz.at
- 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 - © Copyright 2013
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Math. Comp. 83 (2014), 1495-1512
- MSC (2010): Primary 11R16, 11R27, 11D85
- DOI: https://doi.org/10.1090/S0025-5718-2013-02751-2
- MathSciNet review: 3167469