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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2512.12455 |
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Table of Contents:
- Let $n \geq 1$, and let $p : {\bf C} \to {\bf C}$ be a monic polynomial of degree $n$. It was conjectured by Erdős, Herzog, and Piranian that the maximal length of lemniscate $\{z \in {\bf C}: |p(z)| = 1\}$ is attained by the polynomial $p(z) = z^n-1$. In this paper, building upon a previous analysis of Fryntov and Nazarov, we establish this conjecture for all sufficiently large $n$.