Annular regions containing all the zeros of a polynomial

A result due to T & ocirc;ya, Montel and Kuniyeda concerning the location of the zeros of a polynomial statesthat if P(z)=a(n)z(n)+a(n-1)z(n-1)+a(n-2)z(n-2)+<middle dot><middle dot><middle dot>+a(0 )is a polynomial of degree nt hen all its zeros lie in the disk |z| <= (1+A(p)(q))(1/q )where p>1, q>1 with 1/p+1/q=1 and A(p)=(& sum;(n-1)(j=0)divided by aj/an divided by(p))(1/p). In this paper, we refine this result and among other things obtain ring shaped regions containing all the zeros of a polynomial with complex coefficients