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arXiv · 2606.24875

A Degree-Four Lemniscate Path Theorem

Venkata Siddharth Pendyala
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Abstract

We prove the degree-four case of a path problem of Erd\H{o}s, 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 $2$.

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Venkata Siddharth Pendyala. 2026-06-23. A Degree-Four Lemniscate Path Theorem. https://arxiv.org/abs/2606.24875

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