Communications of the
Korean Mathematical Society CKMS

Let $\mathcal P_n$ 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 $P(z)$, $Q(z) \in \mathcal P_n$, does there exist a continuous mapping $r \rightarrow G_r(z)\in \mathcal P_n$ on $[0,1]$ such that $G_0(z)=P(z)$ and $G_1(z)=Q(z)$?

Keywords: convex combination, polynomials, self-reciprocal polynomials, unit circle, zeros

MSC numbers: Primary 30C15; Secondary 26C10