Year: 2026
Type: preprint
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 $q\to1$, one of them is able to engender the following conclusion: for any prime $p\equiv2\pmod{3}$ and any nonnegative integer $s$ subject to $ s\leq (p-2)/3$, \[\sum_{k=s}^{(p+1)/3+s}(6k-1)\frac{(-\frac{1}{3})_{k-s}(-\frac{1}{3})_{k+s}(-\frac{1}{3})_{k}}{(k-s)!(k+s)!k!} \equiv 0\pmod{p^3}.\]
Source: arXiv (Cornell University)
Authors: Wei, Chuanan, Ruan, Guozhu
Institution: Hainan Medical University
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7214276392