Simultaneous prime specializations of polynomials over finite fields
Paul Pollack · Proceedings of the London Mathematical Society · 2008
Recently the author proposed a uniform analogue of the Bateman–Horn conjectures for polynomials with coefficients from a finite field (that is, for polynomials in Fq[T] rather than Z[T]). Here we use an explicit form of the Chebotarev density theorem over function fields to prove this conjecture in particular ranges of the parameters. We give some applications including the solution of a problem posed by Hall.