Representations for complex numbers with integer digits

We present the zeta-expansion as a complex version of the well-known beta-expansion. It allows us to expand complex numbers with respect to a complex base by using integer digits. Our concepts fits into the framework of the recently published rotational beta-expansions. But we also establish relatio...

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Detalles Bibliográficos
Autor principal: Surer, Paul
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer International Publishing 2020
Materias:
Research
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7655639/
https://www.ncbi.nlm.nih.gov/pubmed/33195992
http://dx.doi.org/10.1007/s40993-020-00214-0
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author Surer, Paul
author_facet Surer, Paul
author_sort Surer, Paul
collection PubMed
description We present the zeta-expansion as a complex version of the well-known beta-expansion. It allows us to expand complex numbers with respect to a complex base by using integer digits. Our concepts fits into the framework of the recently published rotational beta-expansions. But we also establish relations with piecewise affine maps of the torus and with shift radix systems.
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spelling pubmed-76556392020-11-12 Representations for complex numbers with integer digits Surer, Paul Res Number Theory Research We present the zeta-expansion as a complex version of the well-known beta-expansion. It allows us to expand complex numbers with respect to a complex base by using integer digits. Our concepts fits into the framework of the recently published rotational beta-expansions. But we also establish relations with piecewise affine maps of the torus and with shift radix systems. Springer International Publishing 2020-11-10 2020 /pmc/articles/PMC7655639/ /pubmed/33195992 http://dx.doi.org/10.1007/s40993-020-00214-0 Text en © The Author(s) 2020 Open AccessThis article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
spellingShingle Research
Surer, Paul
Representations for complex numbers with integer digits
title Representations for complex numbers with integer digits
title_full Representations for complex numbers with integer digits
title_fullStr Representations for complex numbers with integer digits
title_full_unstemmed Representations for complex numbers with integer digits
title_short Representations for complex numbers with integer digits
title_sort representations for complex numbers with integer digits
topic Research
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7655639/
https://www.ncbi.nlm.nih.gov/pubmed/33195992
http://dx.doi.org/10.1007/s40993-020-00214-0
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