Zeros of Harmonic Functions whose Caustic is a Non-Singular Image of an Epicycloid
Complex Variables
2025-08-12 v1
Abstract
Recent researchers have investigated how the zeros of certain families of complex harmonic functions change with a single parameter. Many leverage the well-behaved images of the critical curve and the harmonic analogue of the Argument Principle to prove zero-counting theorems. In this paper, we investigate the zeros of a family of harmonic functions for which the image of its critical curve is a non-singular linear image of an epicycloid. By analyzing this curve and using the harmonic analogue of the Argument Principle, we obtain a detailed zero-counting theorem for our family.
Cite
@article{arxiv.2508.06724,
title = {Zeros of Harmonic Functions whose Caustic is a Non-Singular Image of an Epicycloid},
author = {Eli Sampson},
journal= {arXiv preprint arXiv:2508.06724},
year = {2025}
}