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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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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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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