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A remark on polynomials and the transfinite diameter

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Abstract

The main result is the following theorem: LetE be the point set for which |Π nv=1 (Z-Z V)|<1. If the zerosz ν (ν=1, …,n) belong to a bounded, closed and connected set whose transfinite diameter is 1−c (0<c<1), thenE contains a disk of positive radius ρ, dependent only onc.

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References

  1. P. Erdös, Herzog and G. Piranian,Metric properties of polynomials, J. Analyse Math.6 (1958), 125–148.

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  2. M. Fekete,Ueber die Verteilung der Wurzeln bei gewissen algebraischen Gleichungen mit ganzzahligen Koeffizienten, Math. Z.17 (1923), 228–249.

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  1. Technion-Israel Institute of Technology, Haifa, Israel

    P. Erdös & E. Netanyahu

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  1. P. Erdös
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  2. E. Netanyahu
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Erdös, P., Netanyahu, E. A remark on polynomials and the transfinite diameter. Israel J. Math. 14, 23–25 (1973). https://doi.org/10.1007/BF02761531

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  • DOI: https://doi.org/10.1007/BF02761531

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