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arXiv · 2208.11341

A uniqueness problem concerning entire functions and their derivatives

Andreas Sauer·Andreas Schweizer
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Abstract

We determine all entire functions $f$ such that for nonzero complex values $a\neq b$ the implications $f=a \Rightarrow f' =a$ and $f' =b \Rightarrow f=b$ hold. This solves an open problem in uniqueness theory. In this context we give a normality criterion, which might be interesting in its own right.

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Andreas Sauer, Andreas Schweizer. 2022-08-24. A uniqueness problem concerning entire functions and their derivatives. https://doi.org/10.1007/s40315-023-00486-4

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