On a family of continued fractions in $Q((T^1))$ associated to infinite binary words derived from the Thue-Morse sequence
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866913859674046464 |
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| author | Allombert, Bill Lasjaunias, Alain |
| author_facet | Allombert, Bill Lasjaunias, Alain |
| contents | For each integer n > 1, we present an element in $Q((T^-1))$, having a power series expansion based on an infinite word W(n), over the alphabet ${+1;-1}g and whose continued fraction expansion has a particular pattern which is explicitly described. The word W(1) is the Thue-Morse sequence and the following words are defined in a similar way. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2505_20102 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On a family of continued fractions in $Q((T^1))$ associated to infinite binary words derived from the Thue-Morse sequence Allombert, Bill Lasjaunias, Alain Number Theory 11J70 For each integer n > 1, we present an element in $Q((T^-1))$, having a power series expansion based on an infinite word W(n), over the alphabet ${+1;-1}g and whose continued fraction expansion has a particular pattern which is explicitly described. The word W(1) is the Thue-Morse sequence and the following words are defined in a similar way. |
| title | On a family of continued fractions in $Q((T^1))$ associated to infinite binary words derived from the Thue-Morse sequence |
| topic | Number Theory 11J70 |
| url | https://arxiv.org/abs/2505.20102 |