TITLE: Dirichlet/Chebotarev's Theorem for natural/analytic density
QUESTION [9 upvotes]: A little bird told me that Dirichlet/Chebotarev's Theorem is true not only for Dirichlet density, but also for analytic/natural density. I'm having trouble finding a citation for this. Does anyone know of one?

REPLY [5 votes]: There is a nice treatment of this and discussions of the error term in Serre's book "Lectures on $N_X(p)$". He also gives various applications but I don't think he proves it.
I should note that the natural density version holds over number fields but not over global function fields. Serre discusses this in his book.