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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| Online Access: | https://arxiv.org/abs/2603.11670 |
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| _version_ | 1866911634580045824 |
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| author | Chang, Xiang-Ke Liu, Jiyuan |
| author_facet | Chang, Xiang-Ke Liu, Jiyuan |
| contents | As argued by Hone in the paper [Commun. Pure Appl. Math., 74(11):2310--2347, 2021], a ``mismatch" problem remained unsolved while he was investigating continued fraction expansions and Hankel determinants from hyperelliptic curves. In this paper, by introducing a new notion called quadratic orthogonal pairs for hyperelliptic functions, we resolve the corresponding problem. As further applications, we give a thorough treatment of the initial value problems for two discrete integrable systems, i.e. the bilateral Somos-4 and Somos-5 recurrences. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_11670 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Hankel Determinants from Quadratic Orthogonal Pairs for Hyperelliptic Functions and Their Applications Chang, Xiang-Ke Liu, Jiyuan Exactly Solvable and Integrable Systems Combinatorics As argued by Hone in the paper [Commun. Pure Appl. Math., 74(11):2310--2347, 2021], a ``mismatch" problem remained unsolved while he was investigating continued fraction expansions and Hankel determinants from hyperelliptic curves. In this paper, by introducing a new notion called quadratic orthogonal pairs for hyperelliptic functions, we resolve the corresponding problem. As further applications, we give a thorough treatment of the initial value problems for two discrete integrable systems, i.e. the bilateral Somos-4 and Somos-5 recurrences. |
| title | Hankel Determinants from Quadratic Orthogonal Pairs for Hyperelliptic Functions and Their Applications |
| topic | Exactly Solvable and Integrable Systems Combinatorics |
| url | https://arxiv.org/abs/2603.11670 |