Remarks on zeta functions and K-theory over F1

Abstract

We show that the notion of zeta functions over the field of one element F1, as given in special cases by Soulé, extends naturally to all F1-schemes as defined by the author in an earlier paper. We further give two constructions of K-theory for affine schemes or F 1-rings, we show that these coincide in the group case, but not in general.