An integrality phenomenon
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866915944274591744 |
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| author | Fürnsinn, Florian Radchenko, Danylo Zudilin, Wadim |
| author_facet | Fürnsinn, Florian Radchenko, Danylo Zudilin, Wadim |
| contents | We prove a general statement about the integrality of the sequences generated by a recursion of the following form: $nu_n$ equals a linear combination of $u_{n-1},u_{n-2},\dots,u_0$ with polynomial coefficients in $n$ of special form. This includes a conjectural integrality of the sequence related to the Hörmander-Bernhardsson extremal function, for which we further give a direct proof as well. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_25506 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | An integrality phenomenon Fürnsinn, Florian Radchenko, Danylo Zudilin, Wadim Number Theory Classical Analysis and ODEs Combinatorics 11B83, 33C70, 33E30 We prove a general statement about the integrality of the sequences generated by a recursion of the following form: $nu_n$ equals a linear combination of $u_{n-1},u_{n-2},\dots,u_0$ with polynomial coefficients in $n$ of special form. This includes a conjectural integrality of the sequence related to the Hörmander-Bernhardsson extremal function, for which we further give a direct proof as well. |
| title | An integrality phenomenon |
| topic | Number Theory Classical Analysis and ODEs Combinatorics 11B83, 33C70, 33E30 |
| url | https://arxiv.org/abs/2603.25506 |