3 problems

Let $p$ be a degree-$n$ univariate complex polynomial. Let its DR-circles be the circles centered at the roots of $p'$ with radii $\rho_j$, where … For each root of $p$, consider i…

Let $K$ be a finite extension of the rational field $\mathbb{Q}$ or of the rational function field $\mathbb{F}_p(T)$. Let $(x_n)$ be the Newton approximation sequence associated to…

Let $f$ be a polynomial of degree $d\geq 2$ with coefficients in a number field $K$, and let $x_0\in K$. Define the Newton map … and, for each $n\geq 0$, set … Assume that the Newt…