Remarks to a theorem of Sinclair and Vaaler

Abstract

Sinclair and Vaaler in [6] Theorem 1.2 found sufficient conditions, nonlinear in the coefficients depending on a parameter p 1 , for self-inversive polynomials to have all their zeros on the unit circle. Here we discuss the dependence of the conditions on the parameter and through it we show that applying Theorem 1 of Lakatos and Losonczi [4] their result can be strengthened by giving the locations of the zeros. Mathematics subject classification (2010): 30C15, 12D10, 42C05.