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Proof of Two Conjectural q-Supercongruences Related to Van Hamme's (G.2) Supercongruence
Abstract
In this paper, we prove two conjectures concerning parametric q- supercongruences related to Van Hamme's (G.2) supercongruence. First, we confirm Tang\rq s conjecture \cite[Conjecture $4.1$]{Tang G2} by establishing the corresponding congruences modulo [m]Φm(q)2. Second, we prove a conjecture of Wang and Xu \cite[Conjecture $2$]{WangXu24}, extending their q-supercongruence modulo Φm(q)5 to modulo [m]Φm(q)4 when m≡1pmod4.
Related
- q-Analogues of some supercongruences related to Van Hamme's (E.2) and (F.2) supercongruences
- q-Analogues of some supercongruences related to generalized Van Hamme-type supercongruences
- Proofs of eighteen conjectural identities related to the modulo nine Kanade--Russell identities
- A q-analogue of a binomial supercongruence
- A two-step supercongruence for an Apéry-like sequence
BibTeX
@misc{karmakar2026proof,
title = {{Proof of Two Conjectural $q$-Supercongruences Related to Van Hamme's $\mathrm(G.2)$ Supercongruence}},
author = {Liton Karmakar and Arijit Jana},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.15050},
eprint = {2610.15050},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.15050},
}
RIS
TY - UNPB
TI - Proof of Two Conjectural q-Supercongruences Related to Van Hamme's (G.2) Supercongruence
AU - Liton Karmakar
AU - Arijit Jana
PY - 2026
DA - 2026/10/10
PB - arXiv
DO - 10.48550/arxiv.2610.15050
UR - https://arxiv.org/abs/2610.15050
AB - In this paper, we prove two conjectures concerning parametric q- supercongruences related to Van Hamme's (G.2) supercongruence. First, we confirm Tang\rq s conjecture \cite[Conjecture $4.1$]{Tang G2} by establishing the corresponding congruences modulo [m]Φ_m(q)^2. Second, we prove a conjecture of Wang and Xu \cite[Conjecture $2$]{WangXu24}, extending their q-supercongruence modulo Φ_m(q)^5 to modulo [m]Φ_m(q)^4 when m≡1pmod4.
ER -