Hankel Determinants from Quadratic Orthogonal Pairs for Hyperelliptic Functions and Their Applications
Exactly Solvable and Integrable Systems
2026-05-01 v4 Combinatorics
Abstract
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.
Keywords
Cite
@article{arxiv.2603.11670,
title = {Hankel Determinants from Quadratic Orthogonal Pairs for Hyperelliptic Functions and Their Applications},
author = {Xiang-Ke Chang and Jiyuan Liu},
journal= {arXiv preprint arXiv:2603.11670},
year = {2026}
}
Comments
30 pages, to appear in the Journal of the London Mathematical Society