$q$-Supercongruences from squares of basic hypergeometric series

Victor J. W. Guo; Long Li

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arXiv · 2112.12076

$q$-Supercongruences from squares of basic hypergeometric series

Victor J. W. Guo·Long Li

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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 microscoping 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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Victor J. W. Guo, Long Li. 2021-12-17. $q$-Supercongruences from squares of basic hypergeometric series. https://arxiv.org/abs/2112.12076

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