On the density of irreducible polynomials which generate k-free polynomials over function fields

Abstract

Let M∈Fq[t] be a polynomial, and let k≥2 be an integer. In this note, we will compute the asymptotic density of irreducible monic polynomials P∈Fq[t] for which P+M is not divisible by the kth power of any irreducible polynomial.