On the number of zeros of certain harmonic polynomials

Khavinson, Dmitry; Świa̧tek, Grzegorz

doi:10.1090/S0002-9939-02-06476-6

On the number of zeros of certain harmonic polynomials
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by Dmitry Khavinson and Grzegorz Świa̧tek PDF

Proc. Amer. Math. Soc. 131 (2003), 409-414 Request permission

Abstract:

Using techinques of complex dynamics we prove the conjecture of Sheil-Small and Wilmshurst that the harmonic polynomial $z-\overline {p(z)}$, $\deg p = n > 1$, has at most $3n-2$ complex zeros.

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