Palindromic and perturbed polynomials: zeros location

Abstract

We give necessary and sufficient conditions for all zeros of the palindromic polynomial R(z)=1+lambda(z+z (2)+aEuro broken vertical bar+z (n-1))+z (n) , , to be on the unit circle and we find for which S(z)=R(z)+gamma z (n) , n natural, has all its zeros in the closed unit disc.