7 problems

Let $Q(z)$ be the leading polynomial in the generalized Lamé equation, and let $\alpha_i$ denote its coefficient parameters. Consider the Van Vleck polynomials for this equation wi…

Let $Q(z)$ and $P(z)$ be polynomials with $\deg Q(z)=l\geq 2$ and $\deg P(z)\leq l-1$, and let $\mathcal V_n$ be the finite measure on the space $Pol_{l-2}$ of monic polynomials of…

Let $\mathfrak d(z)=\sum_{i=1}^k Q_i(z)\frac{d^i}{dz^i}$ be a non-degenerate higher Lamé operator, and let $r=\max_{i=1,\ldots,k}(\deg Q_i-i)$. Let $Pol_r$ be the space of monic po…

Let $\mathfrak d(z)=\sum_{i=1}^k Q_i(z)\frac{d^i}{dz^i}$ be a non-degenerate higher Lamé operator, and call $Q_k(z)\frac{d^k}{dz^k}$ its leading term. Van Vleck and Stieltjes polyn…

Let $\mathfrak d(z)=\sum_{i=1}^k Q_i(z)\frac{d^i}{dz^i}$ be a non-degenerate higher Lamé operator, with $r=\max_{i=1,\ldots,k}(\deg Q_i-i)\geq 0$ and $\deg Q_k=k+r$. For each posit…

Consider a generalized Heun equation … where $\deg Q_{k+1}(z)=k+1$ and $\deg Q_i(z)\leq i$ for $i=2,3,\ldots,k$. For each sufficiently large positive integer $n$, let $\mu_n$ be th…

Interlacing conjecture. These distances interlace with those of order $3k+2$: