Abstract
In this paper, in view of the transformation formulae for q-hypergeometric series, a lemma of El Bachraoui, the creative microscoping method developed by Guo and Zudilin and the Chinese remainder theorem for coprime polynomials, we obtain certain q-supercongruences modulo the fifth power of a cyclotomic polynomial from squares of q-hypergeometric series.
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Acknowledgements
We would like to thank V.J.W. Guo and C. Wei for their help and guidance. We also thank the anonymous referee for improving our original manuscript. In particular, we thank the referee for pointing out the q-supercongruence (2.4) due to Guo and Zudilin [11, Theorem 2] and helping us simplify the proofs of Theorems 2.1 and 2.2. The first author was supported by the National Natural Science Foundation of China (Grant No. 11871258). The second author was supported by the National Natural Science Foundation of China (Grant No. 12001376).
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Song, H., Wang, C. Some q-Supercongruences Modulo the Fifth Power of a Cyclotomic Polynomial from Squares of q-Hypergeometric Series. Results Math 76, 222 (2021). https://doi.org/10.1007/s00025-021-01536-w
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DOI: https://doi.org/10.1007/s00025-021-01536-w
Keywords
- q-supercongruence
- creative microscoping
- cyclotomic polynomial
- the Chinese remainder theorem
- q-hypergeometric series