3 problems

Let $(x_n)_{n\geq 1}$ be any sequence of distinct points on the circle $\mathbb T$. For each $n$, let $M_n^{(2)}$ and $m_n^{(2)}$ denote the quantities defined in the paper for two…

Let $\mathbb{S}^1$ be the unit circle, let $\omega_N^*$ denote a configuration of $N$ equally spaced points on it, and let $P_s(\omega_N^*)$ be its Riesz polarization. For…

Ambrus–Ball–Erdős conjecture. The supremum of $F$ is minimized by the regular, equidistant configuration of nodes; after normalizing $y_0=0$, this means