Using Real-Variable Techniques to Study Zeros of Complex-Valued Harmonic Functions
Complex Variables
2025-06-19 v1
Abstract
We investigate the zeros of two one-parameter families of harmonic functions and describe how the number of zeros depends on the parameter. Our functions have the property that all zeros lie on certain rays in the complex plane and thus we are able to use real-variable techniques to count the zeros on each ray.
Cite
@article{arxiv.2506.14966,
title = {Using Real-Variable Techniques to Study Zeros of Complex-Valued Harmonic Functions},
author = {Jennifer Brooks and Mary Jenkins and Samuel Liechty and Kaden Parker and Katherine Perez and Dallin Robison and Eli Sampson and Matthew G. Wilson},
journal= {arXiv preprint arXiv:2506.14966},
year = {2025}
}
Comments
13 pages, 9 figures