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On the order of vanishing at 1 of a polynomial

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Abstract

Suppose thatP(z) is a polynomial of degreen with complex coefficients such that one of its extreme coefficients is maximal in absolute value. We prove that ifn is sufficiently large, then the order of vanishing of the polynomial at a point in the unit circle is less than\(21\sqrt n /13\).

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  1. A. Dubickas
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Partially supported by the Lithuanian State Science and Studies Foundation.

Vilnius University, Naugarduko 24, 2006 Vilnius, Lithuania. Published in Lietuvos Matematikos Rinkinys, Vol. 39, No. 4, pp. 461–468, October–December, 1999.

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Dubickas, A. On the order of vanishing at 1 of a polynomial. Lith Math J 39, 365–370 (1999). https://doi.org/10.1007/BF02465586

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  • DOI: https://doi.org/10.1007/BF02465586

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