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Many lemniscates with large diameter

Published 15 Sep 2025 in math.CV | (2509.11597v1)

Abstract: We prove that for every $0 < c < 4$ and every $N \in \mathbb{N}$ there exists a monic polynomial $p(z) = zn + a_{n-1} z{n-1} + \dots + a_0$ 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 Erd\H{o}s.

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Authors (1)

  1. Linhang Huang 

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