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<p>To the best of our knowledge, the problem of determining the unimodular zeros of complex harmonic polynomials has not been investigated in the existing literature. Recognizing this gap, we formulate and study a subclass of complex harmonic polynomials, focusing on the characterization and distribution of their unimodular zeros. We illustrate our findings through suitable examples and graphical representations, thereby providing both theoretical insight and visual interpretation. In addition, we study the geometric properties of the critical curve under particular settings.</p>

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Unimodular Zeros of Certain Complex Harmonic Polynomials

  • 期刊论文

  • 发表日期：

    2026年4月10日

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  • Adithya Mayya,
  • Sarika Verma,
  • Raj Kumar

摘要

To the best of our knowledge, the problem of determining the unimodular zeros of complex harmonic polynomials has not been investigated in the existing literature. Recognizing this gap, we formulate and study a subclass of complex harmonic polynomials, focusing on the characterization and distribution of their unimodular zeros. We illustrate our findings through suitable examples and graphical representations, thereby providing both theoretical insight and visual interpretation. In addition, we study the geometric properties of the critical curve under particular settings.