Tuples of polynomials over finite fields with pairwise coprimality conditions

Abstract

Let q be a prime power. We estimate the number of tuples of degree bounded monic polynomials (Q1, . . . , Qv) ∈ (Fq[z])v that satisfy given pairwise coprimality conditions. We show how this generalises from monic polynomials in finite fields to Dedekind domains with a finite norm