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PreprintarXiv licencearXiv

q-Analogues of some supercongruences related to Van Hamme's (E.2) and (F.2) supercongruences

  • Liton Karmakar
  • Arijit Jana
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Abstract

In this paper, we present a one-parameter extension of some supercongruences related to Van Hamme's (E.2) and (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 6ϕ5 summation formula.

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Cite

BibTeXRIS
BibTeX
@misc{karmakar2026qanalogues,
  title = {{$q$-Analogues of some supercongruences related to Van Hamme's (E.2) and (F.2) supercongruences}},
  author = {Liton Karmakar and Arijit Jana},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.11786},
  eprint = {2610.11786},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.11786},
}
RIS
TY  - UNPB
TI  - q-Analogues of some supercongruences related to Van Hamme's (E.2) and (F.2) supercongruences
AU  - Liton Karmakar
AU  - Arijit Jana
PY  - 2026
DA  - 2026/10/08
PB  - arXiv
DO  - 10.48550/arxiv.2610.11786
UR  - https://arxiv.org/abs/2610.11786
AB  - In this paper, we present a one-parameter extension of some supercongruences related to Van Hamme's (E.2) and (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 _6ϕ_5 summation formula.
ER  -