2021/12/17 by Victor J. W. Guo, Long Li, Guo, Victor J. W. +1
Mathematics · #Advanced Mathematical Identities #Mathematical functions and polynomials #Analytic Number Theory Research
paper · pdf · doi:10.48550/arxiv.2112.12076
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.