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

Understand

We present a sufficient condition for a self-inversive polynomial to have a fixed number of roots on the complex unit circle.

• We also prove that these roots are simple when that condition is satisfied.
• This generalizes the condition found by Lakatos and Losonczi for all the roots of a self-inversive polynomial to lie on the complex unit circle.