• DOI:10.1137/0522076
Corpus ID: 50466571

Polynomials with nonnegative coefficients whose zeros have modulus one

@article{Evans1991PolynomialsWN,
  title={Polynomials with nonnegative coefficients whose zeros have modulus one},
  author={R. J. Evans and J. R. Greene},
  journal={Siam Journal on Mathematical Analysis},
  year={1991},
  volume={22},
  pages={1173-1182}
}

R. J. Evans, J. R. Greene

Published 1991

Mathematics

Siam Journal on Mathematical Analysis

Define $p(z) = \prod _{j = 0}^{n - 1} (z - e^{i(\theta + \alpha j)} )$ for $\alpha > 0$ and $\theta \geq 0$ with ${\pi / 2} - (n - 1){\alpha / 2} \leq \theta \leq \pi - (n - 1){\alpha / 2}$. It is proved that if $0 < \alpha < {\pi / n}$, then the $2n + 1$ coefficients of $p(z)$ are all positive. It is also proved that if for some point $\theta $, all coefficients of $p(z)$ are nonnegative, then each coefficient is an increasing function of $\theta $ in a neighborhood of this point. A similar… CONTINUE READING

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