{"title":"Bases of $$\\varepsilon $$ -Canonical Number Systems in Quadratic Number Fields","authors":"Borka Jadrijević","doi":"10.1007/s00009-024-02676-3","DOIUrl":null,"url":null,"abstract":"<p>In this paper, we give an explicit characterization of all bases of <span>\\(\\varepsilon \\)</span>-canonical number systems (<span>\\(\\varepsilon \\)</span>-CNS) with finiteness property in quadratic number fields for all values <span>\\(\\varepsilon \\in [0,1)\\)</span>. This result is a consequence of the recent result of Jadrijević and Miletić on the characterization of quadratic <span>\\(\\varepsilon \\)</span>-CNS polynomials. Our result includes the well-known characterization of all bases of classical CNS (<span>\\(\\varepsilon =0\\)</span>) with finiteness property in quadratic number fields. It also fits into the general framework of generalized number systems (GNS) introduced by A. Pethő and J. Thuswaldner.</p>","PeriodicalId":49829,"journal":{"name":"Mediterranean Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":1.1000,"publicationDate":"2024-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mediterranean Journal of Mathematics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s00009-024-02676-3","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
In this paper, we give an explicit characterization of all bases of \(\varepsilon \)-canonical number systems (\(\varepsilon \)-CNS) with finiteness property in quadratic number fields for all values \(\varepsilon \in [0,1)\). This result is a consequence of the recent result of Jadrijević and Miletić on the characterization of quadratic \(\varepsilon \)-CNS polynomials. Our result includes the well-known characterization of all bases of classical CNS (\(\varepsilon =0\)) with finiteness property in quadratic number fields. It also fits into the general framework of generalized number systems (GNS) introduced by A. Pethő and J. Thuswaldner.
期刊介绍：
The Mediterranean Journal of Mathematics (MedJM) is a publication issued by the Department of Mathematics of the University of Bari. The new journal replaces the Conferenze del Seminario di Matematica dell’Università di Bari which has been in publication from 1954 until 2003.
The Mediterranean Journal of Mathematics aims to publish original and high-quality peer-reviewed papers containing significant results across all fields of mathematics. The submitted papers should be of medium length (not to exceed 20 printed pages), well-written and appealing to a broad mathematical audience.
In particular, the Mediterranean Journal of Mathematics intends to offer mathematicians from the Mediterranean countries a particular opportunity to circulate the results of their researches in a common journal. Through such a new cultural and scientific stimulus the journal aims to contribute to further integration amongst Mediterranean universities, though it is open to contribution from mathematicians across the world.
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