2026/03/12 by Xiang-Ke Chang, Jiyuan Liu · 1 voice
Mathematics · Physics and Astronomy · #math.CO #nlin.SI
paper · pdf · doi:10.1112/jlms.70544
arxiv published 2026/03/12 · arxiv updated 2026/04/29
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.