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The Critical Values of a Polynomial

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Constructive Approximation Aims and scope

Abstract.

It has been known for a long time that any real sequence y 1 , . . . ,y n-1 is the sequence of critical values of some real polynomial. Here we show that any complex sequence w 1 , . . . ,w n-1 is the sequence of critical values of some complex polynomial.

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Authors and Affiliations

  1. Centre for Mathematical Sciences Wilberforce Road Cambridge CB3 0WB England afb@dpmms.cam.ac.uk, UK

    Beardon

  2. Centre for Mathematical Sciences Wilberforce Road Cambridge CB3 0WB England tkc@dpmms.cam.ac.uk, UK

    Carne

  3. Department of Mathematics The University of Hong Kong Pokfulam Road Hong Kong ntw@maths.hku.hk, HK

    Ng

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  1. Beardon
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  2. Carne
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  3. Ng
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Beardon, Carne & Ng The Critical Values of a Polynomial . Constr. Approx. 18, 343–354 (2002). https://doi.org/10.1007/s00365-002-0506-1

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  • DOI: https://doi.org/10.1007/s00365-002-0506-1

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