English

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.

Keywords

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

R2 v1 2026-07-01T03:22:45.066Z