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On the number of zeros of certain harmonic polynomials


Authors: Dmitry Khavinson and Grzegorz Swiatek
Journal: Proc. Amer. Math. Soc. 131 (2003), 409-414
MSC (2000): Primary 26C10
DOI: https://doi.org/10.1090/S0002-9939-02-06476-6
Published electronically: September 17, 2002
MathSciNet review: 1933331
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Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

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Additional Information

Dmitry Khavinson
Affiliation: Department of Mathematics, University of Arkansas, Fayetteville, Arkansas 72701
Email: dmitry@comp.uark.edu

Grzegorz Swiatek
Affiliation: Department of Mathematics, Pennsylvania State University, University Park, Pennsylvania 16802
Email: swiatek@math.psu.edu

DOI: https://doi.org/10.1090/S0002-9939-02-06476-6
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
Article copyright: © Copyright 2002 American Mathematical Society

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