Polinômios com raízes no círculo unitário

Abstract

The objective of this work is to characterize the polynomials in Q [x] that have roots in the unitary circle. From this characterization we will estimate how many are these roots. To this end, we will establish a correspondence between the family of palindromic polynomials P (x) of degree 2m and their respective Chebyshev transforms. This will allow us to relate the number of roots of P (x) in the unit circle to the actual roots of the Chebyshev transform of P (x) in the range [-2,2]. Finally, with the aid of the Descartes Signal Rule, we will estimate the amount of roots of the Chebyshev transform in that interval. This work was guided by the title article: "Roots in unity circle" by author KEITH CONRAD.