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<p>We investigate the zeros of a one-parameter family 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.</p>

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

  • 期刊论文

  • 发表日期：

    2026年4月16日

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

摘要

We investigate the zeros of a one-parameter family 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.