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q-Supercongruences from squares of basic hypergeometric series

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Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas Aims and scope Submit manuscript

Abstract

We give some new q-supercongruences on truncated forms of squares of basic hypergeometric series. Most of them are modulo the cube of a cyclotomic polynomial, and two of them are modulo the fourth power of a cyclotomic polynomial. The main ingredients of our proofs are the creative microsco** method, a lemma of El Bachraoui, and the Chinese remainder theorem for coprime polynomials. We also propose several related conjectures for further study.

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Acknowledgements

The authors thank the anonymous referees for careful readings of a previous version of this paper. The second author was partially supported by the National Natural Science Foundation of China (Grant nos. 12201237 and 12271200).

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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 & Long Li

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  1. Victor J. W. Guo
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Guo, V.J.W., Li, L. q-Supercongruences from squares of basic hypergeometric series. Rev. Real Acad. Cienc. Exactas Fis. Nat. Ser. A-Mat. 117, 26 (2023). https://doi.org/10.1007/s13398-022-01364-9

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