Sums of Laurent series with bounded partial quotients
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866917374134845440 |
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| author | Gayfulin, Dmitry Nesharim, Erez |
| author_facet | Gayfulin, Dmitry Nesharim, Erez |
| contents | In 1947 M.Hall proved that every real number is the sum of an integer and two real numbers whose partial quotients are at most $4$. Later, Cusick proved that every real number is the sum of an integer and two real numbers whose partial quotients are at least $2$. In a recent paper, the authors proved that every real number is the sum of two real numbers whose partial quotients diverge. In this paper, we prove an analogue of these results for Laurent series. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2511_11832 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Sums of Laurent series with bounded partial quotients Gayfulin, Dmitry Nesharim, Erez Number Theory 11J61 In 1947 M.Hall proved that every real number is the sum of an integer and two real numbers whose partial quotients are at most $4$. Later, Cusick proved that every real number is the sum of an integer and two real numbers whose partial quotients are at least $2$. In a recent paper, the authors proved that every real number is the sum of two real numbers whose partial quotients diverge. In this paper, we prove an analogue of these results for Laurent series. |
| title | Sums of Laurent series with bounded partial quotients |
| topic | Number Theory 11J61 |
| url | https://arxiv.org/abs/2511.11832 |