On a problem of Ilyeff

Zalman Rubinstein

Vol. 26 (1968), No. 1, 159–161

DOI: 10.2140/pjm.1968.26.159

Abstract

Let P(z) be a polynomial whose zeros z₁,z₂,⋯,z_n (n ≧ 2) lie in |z|≦ 1. It is shown that P′(z) always has a zero in |z − z₁|≦ 1 if |z₁| = 1 or if |z₁| < 1 and n = 3,4.

Mathematical Subject Classification

Primary: 30.11

Milestones

Received: 24 April 1967

Published: 1 July 1968