On some combinations of self-reciprocal polynomials

Abstract

Let P n be the set of all monic integral self-reciprocal polynomials of degree n whose all zeros lie on the unit circle. In this paper we study the following question: For P (z), Q(z) ∈ P n, does there exist a continuous mapping r → G r(z) ∈ P n on [0,1] such that G 0(z) = P (z) and G 1(z) = Q(z)? © 2012 The Korean Mathematical Society.