5 problems

Associate to $Sp_n(\lambda)$ the finite measure … where $\delta(z-a)$ is the Dirac measure supported at $a$. The measure $\mu_n$ is the root-counting measure of the spectral polyno…

Spectral-polynomial identity. The two polynomials are equal:

Let $Q(E)$ be the polynomial whose zeros characterize those values of $E$ for which the equation in the preceding theorem has a solution in the space ${\mathcal F}$, and let…

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…

Let $Q(z)$ have roots $a_1,a_2,a_3$, and let $\mu$ be the limiting root-counting measure from the Shapiro–Tater conjecture. For $i\in\{1,2,3\}$, let $\gamma_i$ be the curve consist…