On some generalisations of Brown's conjecture

Document Type : Research Paper


Department of Mathematics, University of Kashmir, Hazratbal, Srinagar, India


Let $P$ be a complex polynomial of the form $P(z)=z\displaystyle\prod_{k=1}^{n-1}(z-z_{k})$,where $|z_k|\ge 1,1\le k\le n-1$ then $ P^\prime(z)\ne 0$. If $|z|<\dfrac {1}{n}$. In this paper, we present some interesting generalisations of this result.


  • Receive Date: 26 February 2015
  • Revise Date: 24 August 2015
  • Accept Date: 04 July 2016
  • First Publish Date: 08 November 2016