Planar Analytic Functions

Abstract

If a is a point in the domain of convergence of a planar power series f in a single variable x one con expand f into a planar power series in the variable (x-a). One arrives at the notion of planar analytic functions on any domain D in the complex plane. It can be described by sections of the sheaf of planar germs. The k-ary exponential series exp(k,x) has infinite radius of convergence. It is possible to define a planar analogue of the classical zeta-function. As yet a functional equation for it has not been obtained.