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Retracted: Growth of polynomials with prescribed zeros. II. (English) Zbl 1318.30004

Tbil. Math. J. 8, No. 2, 69-74 (2015); retraction note ibid. 8, No. 2, 194 (2015).
Summary: In this paper we consider a class of polynomials \(p(z) = c_nz^n+\sum^n_{j=\mu}c_{n-j}z^{n-j}\), \(1 \leq \mu \leq n\), having all its zeros on \(|z| = k\), \(k \leq 1\). Using the notation \(M(p, t) = \underset{|z|=t}\max |p(z)|\), we measure the growth of \(p\) by estimating \(\Big\{\frac{M(p,t)}{M(p,1)}\Big\}^s\) from above for any \(t \geq 1\), \(s\) being an arbitrary positive integer.
Editorial remark: This paper has been retracted by the authors, see [Zbl 1330.30013] for the retraction note.

MSC:

30A10 Inequalities in the complex plane
30C10 Polynomials and rational functions of one complex variable
30C15 Zeros of polynomials, rational functions, and other analytic functions of one complex variable (e.g., zeros of functions with bounded Dirichlet integral)

Citations:

Zbl 1330.30013
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References:

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