On the Sendov conjecture and the critical points of polynomials

TL;DR

This paper investigates the Sendov conjecture, focusing on polynomials of degree nine, and presents new results concerning the distribution of their critical points.

Contribution

It provides novel insights and partial results on the Sendov conjecture specifically for degree nine polynomials.

Findings

New results on critical points of polynomials

Partial verification of Sendov conjecture for degree nine

Enhanced understanding of polynomial critical point distribution

Abstract

In this paper, we obtain new results on the critical points of a polynomial. We discuss the Sendov conjecture for polynomials of degree nine.