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

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arxiv 2506.14966 v1 pith:WGFVA2RR submitted 2025-06-17 math.CV

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 This is my paper
classification math.CV
keywords zerosfunctionsharmonicreal-variabletechniquesablecertaincomplex
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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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