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A q-analogue of a binomial supercongruence
Abstract
In a recent paper arXiv:2503.20727, Ichino and Prasanna proved a supercongruence for binomial coefficients and related it to representations of GL2 over p-adic rings. We prove a q-analog of this supercongruence using the q-Lucas theorem, from which a strengthening of the main result of loc. cit. can easily be deduced. Our proof also substantially simplifies the original argument of arXiv:2503.20727.
Related
- Proof of Two Conjectural q-Supercongruences Related to Van Hamme's (G.2) Supercongruence
- A two-step supercongruence for an Apéry-like sequence
- Regularity and depth of binomial ideals arising from combinatorics
- Stein's method for negative binomial and hyper-negative-binomial laws, with applications
- Diagonal F-threshold of binomial edge ideals
BibTeX
@misc{gonzalez2026qanalogue,
title = {{A $q$-analogue of a binomial supercongruence}},
author = {Oscar Gonzalez},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.36109},
eprint = {2609.36109},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.36109},
}
RIS
TY - UNPB
TI - A q-analogue of a binomial supercongruence
AU - Oscar Gonzalez
PY - 2026
DA - 2026/09/28
PB - arXiv
DO - 10.48550/arxiv.2609.36109
UR - https://arxiv.org/abs/2609.36109
AB - In a recent paper arXiv:2503.20727, Ichino and Prasanna proved a supercongruence for binomial coefficients and related it to representations of GL_2 over p-adic rings. We prove a q-analog of this supercongruence using the q-Lucas theorem, from which a strengthening of the main result of loc. cit. can easily be deduced. Our proof also substantially simplifies the original argument of arXiv:2503.20727.
ER -