On the zeros of reciprocal polynomials

The purpose of this paper is to study reciprocal polynomials whose zeros are located in certain subsets of the complex plane. Of particular interest are the half planes $\Re z<0$, $\Re z>0$, the positive and negative half-lines and the unit circle. Our main tool is the Chebyshev transform (see, e.g., Lakatos [8]) and a Viéta-like formula for reciprocal polynomials (see Losonczi [12]). Using these, we find necessary conditions, in some cases necessary and sufficient conditions for the reciprocal polynomials to have their zeros in the above sets.