4 problems

Asymptotic cyclicity conjecture.

Serre's cyclicity conjecture.

Let $G$ and $w\in\mathcal{L}^1(\mathbb{T})$ be as in the core-carrier conjecture, let $\mu$ have the form, and let $\operatorname{core}(w)$ denote the core of $w$. For a singular m…

Let $f$in the classical Dirichlet space $\mathcal{D}$ be outer, and let $Z(f)$ denote its boundary zero set. Suppose that $Z(f)$ has logarithmic capacity $0$. Brown and Shields con…