Distribution of constant terms of irreducible polynomials in ℤ_p[x] whose degree is a product of two distinct odd primes

Abstract

We obtain explicit formulas for the number of monic irreducible polynomials with prescribed constant term and degree $q_1q_2$ over a finite field, where $q_1$ and $q_2$ are distinct odd~primes. 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 $q_1$-residue and/or a $q_2$-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. This paper continues work done in [1].