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Two parametric q-supercongruences from a summation formula for q-series
Abstract
With the help of a summation formula for q-series and the creative microscoping method, we shall establish two parametric q-supercongruences. They are both modulo the third power of a cyclotomic polynomial. When q→1, one of them is able to engender the following conclusion: for any prime p≡2pmod3 and any nonnegative integer s subject to $ s\leq (p-2)/3$, ∑k=s(p+1)/3+s(6k−1)((−1/3)k−s(−1/3)k+s(−1/3)k)/((k−s)!(k+s)!k!) ≡ 0pmodp3.
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BibTeX
@misc{wei2026parametric,
title = {{Two parametric q-supercongruences from a summation formula for q-series}},
author = {Chuanan Wei and Guozhu Ruan},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.29986},
eprint = {2609.29986},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.29986},
}
RIS
TY - UNPB
TI - Two parametric q-supercongruences from a summation formula for q-series
AU - Chuanan Wei
AU - Guozhu Ruan
PY - 2026
DA - 2026/09/24
PB - arXiv
DO - 10.48550/arxiv.2609.29986
UR - https://arxiv.org/abs/2609.29986
AB - With the help of a summation formula for q-series and the creative microscoping method, we shall establish two parametric q-supercongruences. They are both modulo the third power of a cyclotomic polynomial. When q→1, one of them is able to engender the following conclusion: for any prime p≡2pmod3 and any nonnegative integer s subject to $ s\leq (p-2)/3$, ∑_k=s^(p+1)/3+s(6k−1)((−1/3)_k−s(−1/3)_k+s(−1/3)_k)/((k−s)!(k+s)!k!) ≡ 0pmodp^3.
ER -