Some new q-congruences for truncated basic
We provide several new q-congruences for truncated basic
hypergeometric series, mostly of arbitrary order.
Our results include congruences modulo the square or the cube
of a cyclotomic polynomial, and in some instances, parametric
These are established by a variety of techniques including
polynomial argument, creative microscoping
(a method recently introduced by the first author in collaboration with
Zudilin), Andrews' multiseries generalization of the Watson transformation,
and induction. We also give a number of related conjectures including
congruences modulo the fourth power of a cyclotomic polynomial.
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