Value distributions of derivatives of K -regular polynomial families
Abstract
Abstract Let $\Omega \in \mathbb C$ be a domain such that $K:= \mathbb C \setminus \Omega $ is compact and non-polar. Let $(q_k)_{k>0}$ be a sequence of polynomials with $n_k$ , the degree of $q_k$ satisfying $n_k \to \infty $ , and let $(q_k^{(m)})_k$ denote the sequence of m th derivatives. We provide conditions which ensure that the preimages $(q_k^{(m)})^{-1}(\{a\})$ uniformly equidistribute on $\partial \Omega $ , as $k \to \infty $ , for every $a \in \mathbb C$ and every $m = 0, 1, \ldots .$
Fields of Study & Subjects
Meromorphic and Entire Functions
Analytic Number Theory Research
Advanced Differential Equations and Dynamical Systems
Publication details
- Journal / source
- Ergodic Theory and Dynamical Systems
- Publisher
- Cambridge University Press (CUP)
- Volume
- 46
- Issue
- 6
- Pages
- 1576–1586
- Publication date
- 18 February 2026
- Language
- EN