Some Results Concerning Sendov Conjecture

Abstract

Let P(z) be a complex polynomial of degree n having all its zeros in |z| ≤ 1. Then the Sendov’s Conjecture states that there is always a critical point of P(z) in |z − a| ≤ 1, where a is any zero of P(z). In this paper, we verify the Sendov’s Conjecture for some special cases. The case where a is the root of pth smallest modulus is also investigated.