This work describes several first steps in extending Tate–Iwasawa’s analytic method
to define an L–function in higher dimensions. For generalizing this method the
author advocates the usefulness of the classical Riemann–Hecke approach, his adelic
complexes together with his generalization of Krichever’s correspondence. He
analyzes dimension 1 types of functions and discusses properties of the lattice of
commensurable classes of subspaces in the adelic space associated to a divisor on an
algebraic surface.
Keywords
L–function, higher dimensional
local fields, adelic complexes
