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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.

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    If $z$ is a zero of $f$ then $a+z$ is a zero of $T_a$, and the converse is also true.2012-05-14
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    I don't get the point of your edit.2012-05-14
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    You mean the ",......"! means "etc."; for more questions/properties comes to your mind.2012-05-14

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