Distribution of Zeros and Critical Points of a Polynomial, and Sendov’s Conjecture

According to the Gauss–Lucas theorem, the critical points of a complex polynomial where always lie in the convex hull of its zeros. In this paper, we prove certain relations between the distribution of zeros of a polynomial and its critical points. Using these relations, we prove the well-known Send...

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Bibliographic Details
Published in:Journal of contemporary mathematical analysis 2023-10, Vol.58 (5), p.384-388
Main Authors: Sofi, G. M., Shah, W. M.
Format: Article
Language:English
Subjects:
Convexity
Critical point
Mathematics
Mathematics and Statistics
Polynomials
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Summary:According to the Gauss–Lucas theorem, the critical points of a complex polynomial where always lie in the convex hull of its zeros. In this paper, we prove certain relations between the distribution of zeros of a polynomial and its critical points. Using these relations, we prove the well-known Sendov’s conjecture for certain special cases.
ISSN:1068-3623
1934-9416
DOI:10.3103/S1068362323050084