A parametric q-congruence for truncated basic hypergeometric series

Let d4d\geqslant4 and let n>1n>1 satisfy n1(modd)n\equiv-1\pmod d. Let (a;q)k(a;q)_k denote the qq-shifted factorial and let Φn(q)\Phi_n(q) be the nnth cyclotomic polynomial. The q-congruence.

k=0n1(aq,a2q2,qd3/a3;qd)k(aqd,a2qd,qd/a3;qd)kqdk0(modΦn(q)).\sum_{k=0}^{n-1}\frac{(aq,a^2q^2,q^{d-3}/a^3;q^d)_k}{(aq^d,a^2q^d,q^d/a^3;q^d)_k}q^{dk}\equiv0\pmod{\Phi_n(q)}.

This is proposed as a new parametric congruence for truncated basic hypergeometric series; no resolution is supplied in the source.

Sources & referencesView supporting material

Primary source

Victor J. W. Guo and Michael J. Schlosser, “Some new q-congruences for truncated basic hypergeometric series: even powers”, arXiv:1904.00490 (2019).

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