The arithmetic structures of the ring of integers Z and the ring of polynomials Fq[x], where q is a prime power, are strikingly similar. In particular, the densities of irreducible elements in these rings are virtually identical, leading to very closely analogous theorems (and conjectures) in the two settings. For a general exposition on the ideas contained in this

and conjectures, listing first the item involving Z and second its analogue in Fq[x]. The latter of these first two definitions will be used throughout this section.