For p(z)=z^m+c(z^k+conj(z)^k)-1, the paper derives exact minimum and maximum zero counts as c varies, using zeros confined to 2m rays and real-valued polynomial counts per ray.
On the zeros of polyanalytic polynomials
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Using Real-Variable Techniques to Study Zeros of Complex-Valued Harmonic Functions
For p(z)=z^m+c(z^k+conj(z)^k)-1, the paper derives exact minimum and maximum zero counts as c varies, using zeros confined to 2m rays and real-valued polynomial counts per ray.