Distribution of constant terms of irreducible polynomials in Zp [x]

We obtain explicit formulas for the number of monic irreducible polynomials with prescribed constant term and degree q(k) over a finite field. These formulas are derived from work done by Yucas. We show that the number of polynomials of a given constant term depends only on whether the constant term is a residue in the underlying field. We further show that as k becomes large, the proportion of irreducible polynomials having each constant term is asymptotically equal.