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arXiv · 2602.11296

On the Parameter Spaces of Harmonic Trinomial Equations

Waldemar Barrera·Lucia Campa·Juan Pablo Navarrete
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Abstract

We analyze the parameter space of harmonic trinomial equations of the form $z^{n+m}+b\overline{z}^m+c$, where $n,m\in\mathbb{Z}^+$ are coprime and $b,c\in\mathbb{C}$. Using versions of the Bohl and Egerv\'ary theorems for harmonic trinomials, we describe the geometric curves in the parameter space that arise when considering a simple root or a multiple root, or when two distinct roots have the same modulus. In particular, we study the geometric properties of these curves, called trochoids.

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Waldemar Barrera, Lucia Campa, Juan Pablo Navarrete. 2026-02-11. On the Parameter Spaces of Harmonic Trinomial Equations. https://arxiv.org/abs/2602.11296

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