On linear combinations of units with bounded coefficients and double-base digit expansions

Let [Formula: see text] be the maximal order of a number field. Belcher showed in the 1970s that every algebraic integer in [Formula: see text] is the sum of pairwise distinct units, if the unit equation [Formula: see text] has a non-trivial solution [Formula: see text]. We generalize this result an...

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Detalles Bibliográficos
Autores principales: Krenn, Daniel, Thuswaldner, Jörg, Ziegler, Volker
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer Vienna 2012
Materias:
Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4370826/
https://www.ncbi.nlm.nih.gov/pubmed/25814773
http://dx.doi.org/10.1007/s00605-012-0443-4
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author Krenn, Daniel
Thuswaldner, Jörg
Ziegler, Volker
author_facet Krenn, Daniel
Thuswaldner, Jörg
Ziegler, Volker
author_sort Krenn, Daniel
collection PubMed
description Let [Formula: see text] be the maximal order of a number field. Belcher showed in the 1970s that every algebraic integer in [Formula: see text] is the sum of pairwise distinct units, if the unit equation [Formula: see text] has a non-trivial solution [Formula: see text]. We generalize this result and give applications to signed double-base digit expansions.
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spelling pubmed-43708262015-03-24 On linear combinations of units with bounded coefficients and double-base digit expansions Krenn, Daniel Thuswaldner, Jörg Ziegler, Volker Mon Hefte Math Article Let [Formula: see text] be the maximal order of a number field. Belcher showed in the 1970s that every algebraic integer in [Formula: see text] is the sum of pairwise distinct units, if the unit equation [Formula: see text] has a non-trivial solution [Formula: see text]. We generalize this result and give applications to signed double-base digit expansions. Springer Vienna 2012-10-06 2013 /pmc/articles/PMC4370826/ /pubmed/25814773 http://dx.doi.org/10.1007/s00605-012-0443-4 Text en © The Author(s) 2012 https://creativecommons.org/licenses/by/4.0/ This article is distributed under the terms of the Creative Commons Attribution License which permits any use, distribution, and reproduction in any medium, provided the original author(s) and the source are credited.
spellingShingle Article
Krenn, Daniel
Thuswaldner, Jörg
Ziegler, Volker
On linear combinations of units with bounded coefficients and double-base digit expansions
title On linear combinations of units with bounded coefficients and double-base digit expansions
title_full On linear combinations of units with bounded coefficients and double-base digit expansions
title_fullStr On linear combinations of units with bounded coefficients and double-base digit expansions
title_full_unstemmed On linear combinations of units with bounded coefficients and double-base digit expansions
title_short On linear combinations of units with bounded coefficients and double-base digit expansions
title_sort on linear combinations of units with bounded coefficients and double-base digit expansions
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4370826/
https://www.ncbi.nlm.nih.gov/pubmed/25814773
http://dx.doi.org/10.1007/s00605-012-0443-4
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