Analysis on arithmetic schemes. I

Abstract

A shift invariant measure on a two dimensional local field, taking values in formal power series over reals, is introduced and discussed. Relevant elements of analysis, including analytic duality, are developed. As a two dimensional local generalization of the works of Tate and Iwasawa a local zeta integral on the topological Milnor $K_2^t$-group of the field is introduced and its properties are studied.