Mathematics > Complex Variables
arXiv:2606.24875 (math)
[Submitted on 23 Jun 2026]
Abstract:We prove the degree-four case of a path problem of Erdős, Herzog, and Piranian. If $f$ is monic of degree four and all zeros of $f$, counted with multiplicity, lie in the open unit disk, then two zeros from this list can be joined inside $$\{z:|f(z)|<1\}$$ by a possibly degenerate polygonal path of length less than $2$.
Submission history
From: Venkata Siddharth Pendyala [view email]
[v1]
Tue, 23 Jun 2026 17:53:23 UTC (3 KB)
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