On the number of roots of self-inversive polynomials on the complex unit circle
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.
KeywordsSelf-inversive polynomials Self-reciprocal polynomials Salem polynomials Bethe Ansatz equations
Mathematics Subject Classification11K16 12D10 12E10 97I80
The author thanks A. Lima-Santos for the motivation, comments, and discussions and also the anonymous referee of this paper for his valuable suggestions.
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