Abstract
Let us denote byΛ n, 1 the supremum of (max∥z∥=1∥p′ n (z)∥)/ (max∥z∥=1∥p n (z)∥) taken over all polynomialsp n of degree at mostn having a zero on the unit circle {z ∈ C∶∥z∥=1}. We show that Λn.1=n-(π 2/16)(1/n)+O(1/n 2.
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Communicated by Edward B. Saff.
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Frappier, C., Rahman, Q.I. & Ruscheweyh, S. On polynomials with a prescribed zero. Constr. Approx 2, 171–177 (1986). https://doi.org/10.1007/BF01893423
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DOI: https://doi.org/10.1007/BF01893423