Characterization of quadratic $\varepsilon$-CNS polynomials (extended version)
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866929256773189632 |
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| author | Jadrijević, Borka Miletić, Kristina |
| author_facet | Jadrijević, Borka Miletić, Kristina |
| contents | In this paper, we give characterization of quadratic $\varepsilon-$canonical number system ($\varepsilon-$CNS) polynomials for all values $\varepsilon \in\lbrack0,1)$. Our characterization provides a unified view of the well-known characterizations of the classical quadratic CNS polynomials ($\varepsilon=0$) and quadratic SCNS polynomials ($\varepsilon=1/2$). This result is a consequence of our new characterization results of $\varepsilon -$shift radix systems ($\varepsilon-$SRS) in the two-dimensional case and their relation to quadratic $\varepsilon-$CNS polynomials. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_16588 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Characterization of quadratic $\varepsilon$-CNS polynomials (extended version) Jadrijević, Borka Miletić, Kristina Number Theory 11A63, 37B10 In this paper, we give characterization of quadratic $\varepsilon-$canonical number system ($\varepsilon-$CNS) polynomials for all values $\varepsilon \in\lbrack0,1)$. Our characterization provides a unified view of the well-known characterizations of the classical quadratic CNS polynomials ($\varepsilon=0$) and quadratic SCNS polynomials ($\varepsilon=1/2$). This result is a consequence of our new characterization results of $\varepsilon -$shift radix systems ($\varepsilon-$SRS) in the two-dimensional case and their relation to quadratic $\varepsilon-$CNS polynomials. |
| title | Characterization of quadratic $\varepsilon$-CNS polynomials (extended version) |
| topic | Number Theory 11A63, 37B10 |
| url | https://arxiv.org/abs/2402.16588 |