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arXiv · 2506.14966

Using Real-Variable Techniques to Study Zeros of Complex-Valued Harmonic Functions

Jennifer Brooks·Mary Jenkins·Samuel Liechty·Kaden Parker·Katherine Perez·Dallin Robison·Eli Sampson·Matthew G. Wilson
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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.

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Jennifer Brooks, Mary Jenkins, Samuel Liechty, Kaden Parker, Katherine Perez, Dallin Robison, Eli Sampson, Matthew G. Wilson. 2025-06-17. Using Real-Variable Techniques to Study Zeros of Complex-Valued Harmonic Functions. https://arxiv.org/abs/2506.14966

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