A result related to the Sendov conjecture

Robert Dalmasso

Type: Article

Publication Date: 2023-01-01

Citations: 0

DOI: https://doi.org/10.4064/ap221118-1-6

Abstract

The Sendov conjecture asserts that if $p(z) = \prod_{j=1}^{N}(z-z_j)$ is a polynomial with zeros $|z_j| \leq 1$, then each disk $|z-z_j| \leq 1$ contains a zero of $p’$. Our purpose is the following: Given a zero $z_j$ of order $n \geq 2$, determine wheth

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Works That Cite This (0)

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Works Cited by This (8)

Action	Title	Year	Authors
+	GENERALIZATION OF A CONJECTURE IN THE GEOMETRY OF POLYNOMIALS	2002	Bl. Sendov
+	A quadratic approximation to the Sendov radius near the unit circle	2004	Michael J. Miller
+	Research Problems in Function Theory	1967	W. K. Hayman
+	Proof of The Sendov Conjecture for Polynomials of Degree at Most Eight	1999	Johnny E. Brown Guangping Xiang
+	Sendov conjecture for high degree polynomials	2014	Jérôme Dégot
+ PDF Chat	On the Zeros of a Polynomial and its Derivative	1969	A. W. Goodman Q. I. Rahman J. S. Ratti
+	Sendov's Conjecture: A note on a paper of Dégot	2018	Taboka Chalebgwa
+ PDF Chat	Sendov’s conjecture for sufficiently-high-degree polynomials	2022	Terence Tao