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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.
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)
Created on August 24, 2014 at 03:18:15. See the history of this page for a list of all contributions to it.