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
Descripción
Sumario: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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