On the zeros of orthogonal polynomials on the unit circle

Let {zn}{zn} be a sequence in the unit disk {z∈C:|z|<1}{z∈C:|z|<1}. It is known that there exists a unique positive Borel measure on the unit circle such that their orthogonal polynomials {Φn}{Φn} satisfy Φn(zn)=0Φn(zn)=0 for each n=1,2,…n=1,2,…. Characteristics of the orthogonality measure and asymptotic properties of the orthogonal polynomials are given in terms of the asymptotic behavior of the sequence {zn}{zn}. Particular attention is paid to periodic sequences of zeros {zn}{zn} with periods two and three.