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Sharp Inequalities for the Zeros of Polynomials and Power Series

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Abstract

Let f be a monic polynomial of degree n with zeros z1,…, z n. We establish sharp estimates for

$$\mathop \sum \limits_{\nu=1}^k \mid z_\nu \mid \quad \quad {\rm and}\quad \quad \mathop \sum \limits_{\nu=1}^k \mid \Im z_\nu \mid \quad \quad (k=1,2,\cdots,n).$$

Results for the zeros of power series are obtained as consequences.

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  1. Mathematical Institute, University of Erlangen-Nuremberg, Bismarckstrasse 1 1/2, D-91054, Erlangen, Germany

    G. Schmeisser

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  1. G. Schmeisser
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Correspondence to G. Schmeisser.

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Schmeisser, G. Sharp Inequalities for the Zeros of Polynomials and Power Series. Results. Math. 39, 333–344 (2001). https://doi.org/10.1007/BF03322693

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  • DOI: https://doi.org/10.1007/BF03322693

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