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Some 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

Inspired by the recent work of El Bachraoui and Guo-Li, we establish several q-supercongruences on the truncated forms of squares of basic hypergeometric series modulo the cube and the fourth power of a cyclotomic polynomial. Our proofs heavily rely on the creative microscoping method devised by Guo and Zudilin, a lemma due to El Bachraoui and the Chinese remainder theorem for coprime polynomials.

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Acknowledgements

We thank the anonymous referees for their careful reading and valuable comments. We also want to thank V.J.W. Guo for informative comments and suggestions. This work is supported by the National Natural Science Foundation of China (Grant No. 12001376) and the Shanghai Rising–Star Program (Grant No. 23QA1407300).

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  1. Department of Mathematics, Shanghai Normal University, Shanghai, 200234, People’s Republic of China

    Hanfei Song & Chun Wang

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  1. Hanfei Song
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  2. Chun Wang
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Correspondence to Chun Wang.

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Song, H., Wang, C. Some q-supercongruences from squares of basic hypergeometric series. Rev. Real Acad. Cienc. Exactas Fis. Nat. Ser. A-Mat. 118, 36 (2024). https://doi.org/10.1007/s13398-023-01534-3

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