Zeros de Polinômios Auto-Recíprocos Reais no Círculo Unitário - Pereira, Junior Augusto [UNESP] (2015)
Classical results of zeros of polynomials are presented, such as more recent results. The interest of this work is to present results on the behavior of zeros of real self-reciprocal polynomial with respect to the unit circle. The behavior of zeros of these polynomials is interesting, because if P(z) is a self-reciprocal polynomial and z0 is a zero of P(z) so the inverse conjugate z0 will be zero of P(z) as well. Known results about necessary and sufficient conditions are presented in order that this class of polynomial has all its zeros on the unit circle, also examples as applications of the results for the best comprehension of the text. In particular two real self-reciprocal polynomial classes are studied, denoted by R( ) n (z) and S( ) n (z), presenting its properties and showing necessary and sufficient conditions so all zeros of both polynomials are on the unit circle