Year: 2026
Type: preprint
Abstract: We prove local asymptotics for near-central complex $(p,q)$-binomial coefficient modulus 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 asymptotics for near-central ratios.
Source: arXiv (Cornell University)
Authors: Åhag, Per, Czyż, Rafał, Lundow, Per-Håkan
Institution: Umeå University
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7167932664