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- W1993997170 abstract "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 result is conjectured for more general polynomials $p(z)$." @default.
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- W1993997170 date "1991-07-01" @default.
- W1993997170 modified "2023-09-25" @default.
- W1993997170 title "Polynomials with Nonnegative Coefficients Whose Zeros Have Modulus One" @default.
- W1993997170 doi "https://doi.org/10.1137/0522076" @default.
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