Different arithmetic theorems. [I.]

Arithmetic and the Incompleteness Theorems

Arithmetic Duality Theorems Second Edition

Addendum/Erratum for Arithmetic Duality Theorems

Then H need not be divisible, i.e., we need not have pH D H . We only know H is contained in pG. Moreover, for x in H , there need not exist an infinite sequence y1;y2;y3:::: such that py2 D y1, py3 D y2; ::. We only know that there exist arbitrarily long finite such sequences. There does exist a unique maximal divisible subgroup D of M , and D is a subgroup of H . Moreover, M DD ̊N where N is a...

Müntz Type Theorems I

In this paper, we concentrate our attention on the Müntz problem in the univariate setting and for the uniform norm. MSC: 41-01, 41-02

Analysis on Arithmetic Schemes . I

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-group of the field is introduced and its properties are st...