Integer translation of meromorphic functions

Abstract

Let G G be a given open set in the complex plane. We prove that there is an entire function such that its integer translations forms a normal family in a neighborhood of z z exactly for z z in G G if and only if G G is periodic with period 1, i.e., z ± 1 ∈ G z\pm 1\in G for all z ∈ G z\in G .