Bases of $$\varepsilon $$ -Canonical Number Systems in Quadratic Number Fields

IF 1.1 3区数学 Q1 MATHEMATICS

Mediterranean Journal of Mathematics Pub Date : 2024-06-16 DOI:10.1007/s00009-024-02676-3

Borka Jadrijević

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.

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二次数域中的$$\varepsilon$$规范数系的基数

在本文中，我们给出了在（0,1）中所有值的二次数域中具有有限性的（$\varepsilon$-规范数系统（$\varepsilon$-CNS）的所有基的明确特征。）这一结果是 Jadrijević 和 Miletić 最近关于二次 $\varepsilon $-CNS多项式特征的结果。我们的结果包括经典 CNS ($\varepsilon =0$)在二次数域中具有有限性的所有基的众所周知的特征。它也符合 A. Pethő 和 J. Thuswaldner 提出的广义数系统 (GNS) 的一般框架。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Mediterranean Journal of Mathematics 数学-数学

CiteScore

1.80

自引率

0.00%

发文量

261

审稿时长

6-12 weeks

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.