4 problems

Rational-summation reduction conjecture. If

For $k,n\in\mathbb{N}_0$, let $G_{k,n}(q)$ be defined by … The polynomials $z_{k,j}(q)$ are to be chosen for $0\le j\le n$. Partial-fraction positivity conjecture for $G_{k,n}(q)$.…

Let $F$ be the function under consideration, with zeros $a_k$ indexed by $k\geq 0$, let $L$ be the derivative order, let $m$ be a positive integer, and let $\omega_m$ denote an $m$…

Let $p_N(n)$ denote the number of partitions of $n$ into at most $N$ parts, and write … with partial-fraction coefficients $C_{h,k,l}(N)$ defined by … Here $s(h,k)$ is the Dedekind…