Record number :

2441410

Title of article :

On some generalisations of Brown's conjecture

Author/Authors :

Ahmad Zargar, Bashir Department of Mathematics - University of Kashmir - Hazratbal, Srinagar , Ahmad, Manzoor Department of Mathematics - University of Kashmir - Hazratbal, Srinagar

Pages :

5

From page :

345

To page :

349

Abstract :

Let B(z; r) denote the open ball in C with centre z and radius r and B(z; r) denote its closure.The
Gauss Lucas Theorem states that every critical point of a complex polynomial P of degree atmost
n lies in the convex hull of its zeros.B. Sendove conjectured that if all the zeros of P lies in B(0; 1)
then for any zero w of P the disk B(w; 1) contains at least one zero of P0 see [4], problem 4.1]. In
connection with this conjecture Brown [3] posed the following problem.

Keywords :

Critical points , Sendove's Conjecture , Coincidence theorem of walsh

Journal title :

Astroparticle Physics

Serial Year :

2016

Link To Document :