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We present a sufficient condition for a self-inversive polynomial to have afixed number of roots on the complex unit circle. We also prove that theseroots are simple when that condition is satisfied. This generalizes thecondition found by Lakatos and Losonczi for all the roots of a self-inversivepolynomial to lie on the complex unit circle.

On the number of roots of self-inversive polynomials on the complex unit circle