Diophantine equations and the generalized Riemann hypothesis

We show that, for a listable set P of polynomials with integer coefficients, the statement “for all roots θ of all polynomials in P, the generalized Riemann hypothesis for Q(θ) holds” is Diophantine. That is, the statement is equivalent to the unsolvability of a particular Diophantine equation. This is achieved by finding a decidable property P such that the aforementioned statement may be written in the form “P holds for all natural numbers”.