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

2025/06/17 by Brooks, Jennifer, Jenkins, Mary, Liechty, Samuel +5 · 2 citations
#30C15 #Complex Variables (math.CV) #FOS: Mathematics

paper · doi:10.48550/arxiv.2506.14966

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.

Citations

• Counting Zeros of Complex-Valued Harmonic Functions via Rouché's Theorem
• Location of the Zeros of Certain Complex-Valued Harmonic Polynomials

Cited by

• Zeros of Harmonic Functions whose Caustic is a Non-Singular Image of an Epicycloid
• Counting Zeros of Complex-Valued Harmonic Functions via Rouché's Theorem

Related

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• Zeros of Harmonic Functions whose Caustic is a Non-Singular Image of an Epicycloid
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