On the zeros of orthogonal polynomials on the unit circle

Let $z_n$ be a sequence in the unit disk $z\in \mathbb{C}:\mathrm{\mid }z\mathrm{\mid }<1$. It is known that there exists a unique positive Borel measure in the unit circle $z\in \mathbb{C}:\mathrm{\mid }z\mathrm{\mid }=1$ such that the orthogonal polynomials ${\mathrm{\Phi }}_n$ satisfy [\Phi_n(z_n)=0] for each $n=1,2,\mathrm{.}\mathrm{.}\mathrm{.}$. Characteristics of the orthogonality measure and asymptotic properties of the orthogonal polynomial are given in terms of asymptotic behavior of the sequence $z_n$. Particular attention is paid to periodic sequence of zeros $z_n$ of period two and three.