# A Proof of Sendov's Conjecture

## TL;DR

This paper provides a proof of Sendov's conjecture, which states that for polynomials with zeros in the unit disk, each zero has a critical point within unit distance, confirming the conjecture's validity.

## Contribution

The paper presents a complete proof of Sendov's conjecture, resolving a long-standing open problem in polynomial zero and critical point distribution.

## Key findings

- Proof of Sendov's conjecture for all polynomials with zeros in the unit disk
- Confirmation that each zero has a critical point within one unit distance
- Advancement in understanding polynomial zero and critical point relationships

## Abstract

The Sendovs conjecture asserts that if all the zeros of a polynomial p(z) lie in the closed unit disk, then there must be a critical point of p(z) within unit distance of each zero. The conjecture has been proved to be true for many special cases.Here we give a proof of the conjecture.