PreprintarXiv licencearXiv
On (p,q)-binomial coefficient ratios for complex parameters
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 √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 n3/4. 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.
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BibTeX
@misc{ahag2026pqbinomial,
title = {{On $(p,q)$-binomial coefficient ratios for complex parameters}},
author = {Per Åhag and Rafał Czyż and Per-Håkan Lundow},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2607.08163},
eprint = {2607.08163},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.08163},
}
RIS
TY - UNPB
TI - On (p,q)-binomial coefficient ratios for complex parameters
AU - Per Åhag
AU - Rafał Czyż
AU - Per-Håkan Lundow
PY - 2026
DA - 2026/10/22
PB - arXiv
DO - 10.48550/arxiv.2607.08163
UR - https://arxiv.org/abs/2607.08163
AB - 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 √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.
ER -