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Another Family of q-Congruences Modulo the Square of a Cyclotomic Polynomial

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Abstract

Using Bailey’s \(_{10}\phi _9\) transformation formula, we prove a family of q-congruences modulo the square of a cyclotomic polynomial, which were previously observed by the author and Zudilin (J Math Anal Appl 475:1636–1646, 2019). As an application, we confirm a conjecture in (Electron Res Arch 28:1031–1036, 2020). This also partially reproves a special case of Swisher’s (H.3) conjecture.

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Acknowledgements

The author thanks Michael J. Schlosser and the anonymous referee for helpful comments on this paper.

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  1. School of Mathematics and Statistics, Huaiyin Normal University, Huai’an, 223300, Jiangsu, People’s Republic of China

    Victor J. W. Guo

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The author was partially supported by the National Natural Science Foundation of China (Grant 11771175).

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Guo, V.J.W. Another Family of q-Congruences Modulo the Square of a Cyclotomic Polynomial. Results Math 76, 109 (2021). https://doi.org/10.1007/s00025-021-01423-4

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