Volume 35, Issue 4
Some Estimates of the Maximum Modulus for Polynomials with Gaps

Eze R. Nwaeze

10.4208/ata.OA-2018-0017

Anal. Theory Appl., 35 (2019), pp. 421-426.

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  • Abstract

Let $p(z)$ be a polynomial of degree $n$ having some zeros at a point $z_0\in\mathbb{C}$ with $|z_0|<1$ and the rest of the zeros lying on or outside the boundary of a prescribed disk. In this brief note, we consider this class of polynomials and obtain some bounds for $\left(\max_{|z|=R}|p(z)|\right)^s$ in terms of $\left(\max_{|z|=1}|p(z)|\right)^s$ for any $R\geq 1$ and $s\in\mathbb{N}.$

  • History

Published online: 2020-01

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