10 problems

Let $F\in\mathcal F_f$ be an admissible compact set for $f$, and let $\{\Omega_n\}$ be an interpolation table disjoint from $F$. Assume that the limiting density $\omega$ in the in…

Tran's conjecture. Every zero of every polynomial $P_n(z)$ lies on $\mathcal C$, and the zeros become dense in $\mathcal C$ as $n\to\infty$.

Let … with $a\in(0,1)$ and $|z_j|\leq 1$ for $j=1,\ldots,n-1$. Sendov's reformulated conjecture. The disk … contains a critical point of $P(z)$. This is a reformulation obtained us…

Let $\mu$ be a finite Borel measure supported on a compact subset $K$ of the real line and assume that $\mu$ is regular in the sense of Stahl and Totik on $K$. Let…

Minkowski's zero-distribution discrepancy conjecture. As $j$ tends to infinity,

Minkowski's orthogonal-polynomial zero convergence conjecture. As $j$ tends to infinity, the zeros $\zeta_l^j$ converge uniformly to the zeros $\theta_l^j$; moreover, there exist p…

Zero-spacing conjecture. For each $\gamma=(\gamma_k)_{k=1}^\infty$ with $\inf_k\gamma_k>0$, $(A_{2^k})_{k=1}^\infty$ is unbounded. If $s=2^k$ for some $k\in\mathbb{N}$, there is a…

Let $\Xi_k(z)=\sum_{j=1}^{k}\Phi_j(z)$ and let $\Phi_{k+1}(z)$ be the next summand in the truncated Riemann Xi-function series. For $k\geq1$ and $0\leq t\leq1$, consider…

Let $a>0$ be a fixed real number, and let $Q$ denote the first quadrant of the complex plane. A function has monotonic zeros in $Q$ when its zeros there, listed by increasing real…

Let $Q$ denote the first quadrant of the complex plane, and let $\Xi_{\Delta,N}(z)$ be the truncation after $N$ terms of the hyperbolic-gamma-function series defining the Ramanujan…