I recently learned the Chebotarev Density Theorem for global fields.
As far as I have seen, all applications of CDT seem to focused around proving some set of prime ideals (or places in function field case) is infinite.
I wished to ask whether there is any quantitative aspect to this. While the existence of density $\delta(A)$ and being non-zero is enough to say that $A$ is infinite, what purpose does the number $\delta(A)$ serve.
More precisely, would someone care to give an application where we somehow use the density.