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On the zeros of Gonchar polynomials

Author: Martin Lamprecht
Journal: Proc. Amer. Math. Soc. 141 (2013), 2763-2766
MSC (2010): Primary 33B99
Published electronically: April 10, 2013
MathSciNet review: 3056566
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Abstract: We verify two conjectures of Brauchart et al. concerning the zeros of the Gonchar polynomials $ G(d;z) := \left [(z-1)^{d}-z-1\right ]z^{d-1} + (z-1)^{d}$, where $ d\in \mathbb{N}$.

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

  • 1. J. S. Brauchart, P. D. Dragnev, E. B. Saff, and C. E. van de Woestijne, A fascinating polynomial sequence arising from an electrostatics problem on the sphere, Acta Math. Hungar. 137 (2012), no. 1-2, 10-26. MR 2966976

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Additional Information

Martin Lamprecht
Affiliation: Institut für Mathematik, Universität Würzburg, Campus Hubland Nord, Emil- Fischer-Strasse 30/40, 97074 Würzburg, Germany
Address at time of publication: Department of Computer Science and Engineering, European University of Cyprus, 6, Diogenous Street, Engomi, P. O. Box 22006, 1516 Nicosia, Cypress

Received by editor(s): October 31, 2011
Published electronically: April 10, 2013
Additional Notes: The author would like to thank Ed Saff for introducing him to the fascinating sequence of Gonchar polynomials.
Communicated by: Walter Van Assche
Article copyright: © Copyright 2013 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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