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.References
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Additional Information
- Dmitry Khavinson
- Affiliation: Department of Mathematics, University of Arkansas, Fayetteville, Arkansas 72701
- MR Author ID: 101045
- Email: dmitry@comp.uark.edu
- Grzegorz Świa̧tek
- Affiliation: Department of Mathematics, Pennsylvania State University, University Park, Pennsylvania 16802
- Email: swiatek@math.psu.edu
- Received by editor(s): May 1, 2001
- Published electronically: September 17, 2002
- Additional Notes: The first author was partially supported by an NSF grant DMS-0139008
The second author was partially supported by an NSF grant DMS-0072312 - Communicated by: Juha M. Heinonen
- © Copyright 2002 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 131 (2003), 409-414
- MSC (2000): Primary 26C10
- DOI: https://doi.org/10.1090/S0002-9939-02-06476-6
- MathSciNet review: 1933331