4 problems

Let $\mathcal{P}_n$ be the real polynomials of degree at most $n$, let $\mu\geq 0$ be a majorant on $[-1,1]$, and define … Let $\omega_\mu$ denote the associated snake polynomial.…

Kroó–Peherstorfer–Saff conjecture. Each function $p\mapsto x_{n,j}(p)$ is increasing on $(0,\infty]$ for $j=1,\dots,k$. The conjecture concerns how the roots of the unique $L^p$-ex…

Dimitrov's conjecture. These polynomials are univalent and solve Dimitrov's problem. The conjecture concerns the extremal polynomials introduced in the cited work and, in particula…

Let $d\geq 17$ be prime with $d\equiv 5\pmod 6$. Define … Let an algebraic integer of degree $d$ that is not a root of unity be extremal if it has the minimum possible house among…