nLab arithmetic zeta function

Idea

Under the function field analogy one understands the Riemann zeta function and Dedekind zeta function as associated to arithmetic curves, hence to spaces in arithmetic geometry of dimension 1. As one passes to higher dimensional arithmetic geometry the corresponding generalization are the arithmetic zeta functions.

References

• Wikipedia, Arithmetic zeta function

• Ivan Fesenko, Adelic approch to the zeta function of arithmetic schemes in dimension two, Moscow Math. J. 8 (2008), 273–317 (pdf)