Almost periodic divisors, holomorphic functions, and holomorphic mappings

Abstract

We prove that to each almost periodic, in the sense of distributions, divisor d in a tube T Ω⊂ C m one can assign a cohomology class from H 2(K, Z) (actually, the first Chern class of a special line bundle over K generated by d) such that the trivial cohomology class represents the divisors of all almost periodic holomorphic functions on T Ω ; here K is the Bohr compactification of R m . This description yields various geometric conditions for an almost periodic divisor to be the divisor of a holomorphic almost periodic function. We also give a complete description for the divisors of homogeneous coordinates for holomorphic almost periodic curves; in particular, we obtain a description for the divisors of meromorphic almost periodic functions.