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

被引：0

作者：

Sofi, G. M. ^{[1
]}

Shah, W. M. ^{[1
]}

机构：

[1] Cent Univ Kashmir, Kashmir, India

来源：

JOURNAL OF CONTEMPORARY MATHEMATICAL ANALYSIS-ARMENIAN ACADEMY OF SCIENCES | 2023年 / 58卷 / 05期

关键词：

polynomials; zeros; critical points;

D O I：

10.3103/S1068362323050084

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

According to the Gauss-Lucas theorem, the critical points of a complex polynomial p(z):= Sigma(n )(j=0)a(j)z(j) where a(j) 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.

引用

页码：384 / 388

页数：5

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