Cyclonomials and Irreducible Polynomials over a Finite Field and their Zeros

A number of properties is derived concerning the distribution of irreducible polynomials in the ring GF(q)[x] as factors of cyclonomials. Furthermore, it is proven that the number of irreducible polynomials of degree m and with trace τ in GF(q)[x] is the same for all values of τ, if q is a prime and m is not a multiple of q. The same appears to be true if m is a multiple of q for all values of τ is not equal to 0.