The Ramanujan Journal

, Volume 42, Issue 2, pp 363–369 | Cite as

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

  • R. S. Vieira


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.


Self-inversive polynomials Self-reciprocal polynomials Salem polynomials Bethe Ansatz equations 

Mathematics Subject Classification

11K16 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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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.Departamento de FísicaUniversidade Federal de São CarlosSão CarlosBrazil

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