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Some New q-Congruences for Truncated Basic Hypergeometric Series: Even Powers
Victor J W Guo1, Michael J Schlosser2
11School of Mathematics and Statistics, Huaiyin Normal University, Huai'an, 223300 Jiangsu People's Republic of China.
Abstract:
We provide several new q-congruences for truncated basic hypergeometric series with the base being an even power of q. Our results mainly concern congruences modulo the square or the cube of a cyclotomic polynomial and complement corresponding ones of an earlier paper containing q-congruences for truncated basic hypergeometric series with the base being an odd power of q. We also give a number of related conjectures including q-congruences modulo the fifth power of a cyclotomic polynomial and a congruence for a truncated ordinary hypergeometric series modulo the seventh power of a prime greater than 3.
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