$q$-Analogues of some supercongruences related to Van Hamme's (E.2) and (F.2) supercongruences
Year: 2026
Type: preprint
Abstract: In this paper, we present a one-parameter extension of some supercongruences related to Van Hamme's $\mathrm{(E.2)}$ and $\mathrm{(F.2)}$ supercongruences. To deduce these results, we first establish the corresponding $q$-supercongruences modulo the third power of a cyclotomic polynomial. Our proofs rely on the \emph{creative microscoping} method devised by Guo and Zudilin~\cite{guo2019q}, together with Jackson's ${}_{6}ϕ_{5}$ summation formula.
Source: arXiv (Cornell University)
Authors: Karmakar, Liton, Jana, Arijit
Institution: National Institute Of Technology Silchar
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7221137834