Almost periodic divisors, holomorphic functions, and holomorphic mappings

Details Almost periodic divisors, holomorphic functions, and holomorphic mappings Almost periodic divisors, holomorphic functions, and holomorphic mappings

2007-01-28

arxiv.org/abs/math/0701819v1

Bulletin des Sciences Mathematiques, v.127 (2003), 859-883

Mathematics

Complex Variables

Scientific paper

We prove that to each almost periodic (in the sense of distributions) divisor in a tube one can assign a first Chern class of a special line bundle over Bohr's compact set generated by the divisor such that the trivial cohomology class represents divisors of all almost periodic holomorphic functions on a tube. 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.

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