Periodicity of general multidimensional continued fractions using repetend matrix form
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866909206410428416 |
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| author | Řada, Hanka Starosta, Štěpán Kala, Vítězslav |
| author_facet | Řada, Hanka Starosta, Štěpán Kala, Vítězslav |
| contents | We consider expansions of vectors by a general class of multidimensional continued fraction algorithms. If the expansion is eventually periodic, then we describe the possible structure of a matrix corresponding to the repetend, and use it to prove that a number of vectors has an eventually periodic expansion in the Algebraic Jacobi--Perron Algorithm. Further, we give criteria for vectors to have purely periodic expansions; in particular, the vector cannot be totally positive. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_00898 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Periodicity of general multidimensional continued fractions using repetend matrix form Řada, Hanka Starosta, Štěpán Kala, Vítězslav Number Theory 11A55, 11J70 We consider expansions of vectors by a general class of multidimensional continued fraction algorithms. If the expansion is eventually periodic, then we describe the possible structure of a matrix corresponding to the repetend, and use it to prove that a number of vectors has an eventually periodic expansion in the Algebraic Jacobi--Perron Algorithm. Further, we give criteria for vectors to have purely periodic expansions; in particular, the vector cannot be totally positive. |
| title | Periodicity of general multidimensional continued fractions using repetend matrix form |
| topic | Number Theory 11A55, 11J70 |
| url | https://arxiv.org/abs/2307.00898 |