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Some q-Supercongruences from a Quadratic Transformation by Rahman

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Abstract

Inspired by the recent work on q-congruences and a quadratic transformation formula of Rahman, we provide some new q-supercongruences. By taking parameters specialization in one of our results, we obtain a new Ramanujan-type supercongruence, which has the same right-hand side as Van Hamme’s (G.2) supercongruence for \(p\equiv 1 \pmod 4\). We also formulate some related challenging conjectures on supercongruences and q-supercongruences.

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Acknowledgements

The authors thank the anonymous referee for many valuable comments on a previous version of this manuscript.

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  1. Department of Mathematics, Shanghai University, Shanghai, 200444, People’s Republic of China

    Yudong Liu & Xiaoxia Wang

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  1. Yudong Liu
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  2. Xiaoxia Wang
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Correspondence to Xiaoxia Wang.

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This work is supported by National Natural Science Foundations of China (11661032).

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Liu, Y., Wang, X. Some q-Supercongruences from a Quadratic Transformation by Rahman. Results Math 77, 44 (2022). https://doi.org/10.1007/s00025-021-01563-7

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