Some new q-congruences for truncated basic
hypergeometric series: even powers
(13 pages)
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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