Given an entire function $f(z)$, and $0\neq a\in \mathbb R$. We define the translation operator: $T_{a}f(z)=f(z-a).$ What properties the new function $f(z-a)$ could have? It is entire function! What about the zeros of $f(z-a)$?
I know it is an open question, but anything you know could help me.