A Note on a result due to Ankeny and Rivlin

2016/10/26 by Eze R. Nwaeze, Nwaeze, Eze R.
Mathematics · #Advanced Differential Equations and Dynamical Systems #Analytic and geometric function theory #Complex Variables (math.CV) #FOS: Mathematics #Meromorphic and Entire Functions

paper · pdf · doi:10.48550/arxiv.1610.08159

openalex publication_date 2016/10/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let p(z)=a₀+a₁z+a₂z²+a₃z³+⋯+a_nzⁿ be a polynomial of degree n having no zeros in the unit disk. ~Then it is well known that for R≥ 1, max_|z|=R|p(z)|≤ (\dfracRⁿ+12)max_|z|=1|p(z)|. In this paper, we consider polynomials with gaps, having all its zeros on the circle S(0, K):=\z: |z|=K\, ~0

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