Extensions of Vieira’s theorems on the zeros of
self-inversive polynomials

Abstract. Recently R.S. Vieira [18] found sufficient conditions for self-inversive polynomials to have some of their zeros on the unit circle. We extend his results by giving the location of those zeros. In case of fourth degree real reciprocal polynomials we compare Vieira's sufficient conditions with the necessary and sufficient conditions obtained by help of Chebyshev transformation.