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This investigation demonstrates the count and distribution of zeros in a generalized harmonic trinomial, highlighting mathematical implications.
We investigate the count and placement of zeros of a generalized complex harmonic trinomial Pc(z). In particular, we prove that Pc(z) has $$(n+2k+j+1)$$ number of zeros. Also, we obtain that sense-preserving and sense-reversing areas of Pc(z) lie in annular regions that enclose the critical curve of Pc(z) . At last we locate the zeros of Pc(z) and obtain annular sectors containing zeros of Pc(z). We demonstrate our findings with examples and figures.
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Mayya et al. (2026) studied this question.
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