Integer translation of meromorphic functions

Kim, Jeong; Rubel, Lee

doi:10.1090/S0002-9947-97-01504-3

Integer translation of meromorphic functions
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by Jeong H. Kim and Lee A. Rubel PDF

Trans. Amer. Math. Soc. 349 (1997), 1447-1462 Request permission

Abstract:

Let $G$ 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 $z$ exactly for $z$ in $G$ if and only if $G$ is periodic with period 1, i.e., $z\pm 1\in G$ for all $z\in G$.

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