6 problems

Resultant stability conjecture. For any positive integers $n,m$ such that $n\leq m$, and any $a>0$, the resultant $\operatorname{res}_z(P_n(s,z),P_m(s+a,z))$ is stable.

Let $n,k\in\mathbb{N}$ and $m\in\mathbb{N}_0$. Laguerre polynomial divisibility conjecture. If the Laguerre polynomial $L_k$ divides the generalized Laguerre polynomial $L_n^{(m)}$…

For $n=0,1,\dots$ and $\alpha>-1$, define the transitional Laguerre polynomials $\widehat{L}^{(\alpha)}_{n+1}(\cdot,t)$ by … where … Let the extreme zeros denote the smallest and l…

Let $n\ge1$, $\alpha=(\alpha_1,\dots,\alpha_n)\in\mathbb N^n$, and $a=(a_1,\dots,a_n)\in(0,+\infty)^n$ be as in the Laguerre-integral conjecture, and let $K_\alpha(a)$ denote the c…

Let $b1>-1$, let $bb$ be an even partition, and let $bc$ be the partition parameter occurring in the generalized Laguerre polynomial $a9_{bb,bc}^{(b1)}$. The zeros of…

Let ${\bf k}\in\mathbb N^n$, and let $L^{[\bf k]}_\alpha(z)$ denote the generalized Laguerre polynomials for multi-indices $\alpha\in\mathbb N^n$. Let $\mathcal M$ be the subspace…