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Licensed Unlicensed Requires Authentication Published online by De Gruyter February 20, 2024

q-supercongruences from Watson's 8φ7 transformation

  • Xiaoxia Wang and Chang Xu EMAIL logo
From the journal Forum Mathematicum

Abstract

Employing Watson’s ϕ 7 8 transformation formula, we unearth several q-supercongruences with a parameter s. Particularly, one of our results is an extension of a q-analogue of Van Hamme’s (G.2) supercongruence. In addition, we obtain a q-supercongruence modulo the fifth power of a cyclotomic polynomial and propose two related conjectures.

MSC 2020: 33D15; 11A07; 11B65

Communicated by Freydoon Shahidi


Award Identifier / Grant number: 12371328

Award Identifier / Grant number: 12371331

Award Identifier / Grant number: 22ZR1424100

Funding statement: This work is supported by National Natural Science Foundations of China (12371328 and 12371331) and Natural Science Foundation of Shanghai (22ZR1424100).

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Received: 2023-11-13
Revised: 2024-02-01
Published Online: 2024-02-20

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