3 problems

Let a proper $q$-hypergeometric multi-dimensional sum be a proper $q$-hypergeometric sum in multiple variables, and let its associated $q$-holonomic module be the corresponding mod…

Let $d\geqslant 3$ and let $n>1$ be an integer with $n\equiv 1\pmod{d}$. With $(a;q)_k=(1-a)(1-aq)\cdots(1-aq^{k-1})$, $[m]=1+q+\cdots+q^{m-1}$, and $\Phi_n(q)$ the $n$-th cyclotom…

Let $d\geqslant 3$ and let $n$ be a positive integer with $n\equiv -1\pmod{d}$. Let $(a;q)_k=(1-a)(1-aq)\cdots(1-aq^{k-1})$ denote the $q$-shifted factorial, let…