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arXiv · 2607.08163

On $(p,q)$-binomial coefficient ratios for complex parameters

Per Åhag·Rafał Czyż·Per-Håkan Lundow
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Abstract

We prove local asymptotics for near-central complex $(p,q)$-binomial coefficient moduli ratios allowing an imaginary parameter perturbation of order $n^{-3/4}$ at a $\sqrt{n}$ length scale from the centre. Moreover, we obtain ratio asymptotics for a smaller imaginary perturbation of order $n^{-5/4}$ at the length scale $n^{3/4}$. These results were obtained by reducing the two-parameter coefficients to just one parameter, giving a branch-free logarithmic representation of the second-order ratio and, hence, uniform complex curvature asymptotes for near-central ratios.

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Per Åhag, Rafał Czyż, Per-Håkan Lundow. 2026-07-10. On $(p,q)$-binomial coefficient ratios for complex parameters. https://arxiv.org/abs/2607.08163

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