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A Further q-Analogue of Van Hamme’s (H.2) Supercongruence for Any Prime \(p\equiv 1\pmod {4}\)

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Abstract

Several years ago, Long and Ramakrishna (Adv Math 290: 773–808, 2016) extended Van Hamme’s (H.2) supercongruence to the modulus \(p^3\) case. Recently, Guo found a q-analogue of the Long–Ramakrishna formula for \(p\equiv 3\pmod 4\). In this note, a q-analogue of the Long–Ramakrishna formula for \(p\equiv 1\pmod 4\) is derived through the q-Whipple formulas and the Chinese remainder theorem for coprime polynomials.

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Acknowledgements

The author is grateful to Chen Wang for his help in the proof of Proposition 1.3.

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  1. Key Laboratory of Data Science and Intelligence Education of Ministry of Education, Hainan Normal University, Haikou, China

    Chuanan Wei

  2. School of Mathematics and Statistics, Hainan Normal University, Haikou, China

    Chuanan Wei

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  1. Chuanan Wei
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Correspondence to Chuanan Wei.

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This work is supported by the National Natural Science Foundations of China (Nos. 12071103 and 11661032).

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Wei, C. A Further q-Analogue of Van Hamme’s (H.2) Supercongruence for Any Prime \(p\equiv 1\pmod {4}\). Results Math 76, 92 (2021). https://doi.org/10.1007/s00025-021-01402-9

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