4 problems

Strengthened Hawaii conjecture. There exists $\sigma\in\mathbb{R}$ such that

Real-root location conjecture. The inequality $x_0>\max(S_1)$ holds if and only if

Bounded-roots conjecture. Every complex root of $p_S(z)$ lies in

Suppose that $f(z)=z^n$, where $n\in\mathbb{N}$ and $n\geq r+1$, and let $P_c$ denote the Taylor polynomial of $f$ of order $r$ at $x=c$. Polynomial-power conjecture. Every pair of…