# Proof of the Sendov conjecture for polynomials of degree nine

## TL;DR

This paper proves the Sendov conjecture specifically for degree nine polynomials, introducing a novel approach to establish upper bounds for the sum of distances to zeros.

## Contribution

It provides the first proof of the Sendov conjecture for degree nine polynomials using a new bounding technique.

## Key findings

- Confirmed the Sendov conjecture for degree nine polynomials.
- Developed a new method to bound the sum of distances to zeros.
- Enhanced understanding of polynomial zero distributions.

## Abstract

In this paper, we prove the Sendov conjecture for polynomials of degree nine. We use a new idea to obtain new upper bound for the $\sigma-$sum to zeros of the polynomial.