Year: 2025
Type: preprint
Abstract: We prove that for every $0 < c < 4$ and every $N \in \mathbb{N}$ there exists a monic polynomial $p(z) = z^n + a_{n-1} z^{n-1} + \dots + a_0$ such that the set $\{z \in \mathbb{C} : |p(z)| \leq 1\}$ has at least $N$ connected components with diameter at least $c$. This answers a question of Erdős.
Source: arXiv (Cornell University)
Author: Huang, Linhang
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4415314768
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