On the zeros of Gonchar polynomials
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- by Martin Lamprecht PDF
- Proc. Amer. Math. Soc. 141 (2013), 2763-2766 Request permission
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
- 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, DOI 10.1007/s10474-012-0195-6
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
- Email: martin.lamprecht@mathematik.uni-wuerzburg.de, m.lamprecht@euc.ac.cy
- 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
- © Copyright 2013
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 141 (2013), 2763-2766
- MSC (2010): Primary 33B99
- DOI: https://doi.org/10.1090/S0002-9939-2013-11866-6
- MathSciNet review: 3056566