I'm not aware of such a theorem, but you should take a look into absolute zeta-functions, which hope to prove a lot about zeta-functions — perhaps up to Riemann's Hypothesis.

Since I don't know much, I better refer you to another MO question:

• What is the field with one element?

I'm not aware of such a theorem, but you should take a look into absolute zeta-functions, which hope to prove a lot about zeta-functions — perhaps up to Riemann's Hypothesis.

Since I don't know much, I better refer you to another MO question:

• What is the field with one element?