On generalisation of Brown's conjecture

Document Type : Research Paper


Department of Mathematics, University of Kashmir, South Campus, Anantnag-192101, Jammu and Kashmir, India


Let  $P$ be the complex polynomial of the form $P(z) = z \prod_{j=1}^{n-1}(z-z_{j})$, with $|z_{j}|\geq 1$, $1 \leq j \leq n-1.$ Then according to famous Brown's Conjecture $p'(z) \neq 0$, for $|z| < \frac{1}{n}.$ This conjecture was proved by Aziz and Zarger [1]. In this paper, we present some interesting generalisations of this conjecture and the results of several  authors related to this conjecture.