论文标题
整数 - 可值得的功能，Hurwitz功能和相关主题：一项调查
Integer--valued functions, Hurwitz functions and related topics: a survey
论文作者
论文摘要
整数函数是整个功能，它将非负整数$ \ Mathbb n $映射到整数。一个例子是$ 2^z $。 Hurwitz函数是一个完整的功能，所有衍生词都以$ 0 $为$。一个示例是$ {\ mathrm e}^z $。此类功能的增长顺序的下限具有丰富的历史。已经考虑了许多变体：例如，假设整数上的第一个$ K $衍生品是整数，或者假设$ k $点的衍生物是整数。这些以及许多其他变体都被考虑。我们调查其中一些。
An integer--valued function is an entire function which maps the nonnegative integers $\mathbb N$ to the integers. An example is $2^z$. A Hurwitz function is an entire function having all derivatives taking integer values at $0$. An example is ${\mathrm e}^z$. Lower bound for the growth order of such functions have a rich history. Many variants have been considered: for instance, assuming that the first $k$ derivatives at the integers are integers, or assuming that the derivatives at $k$ points are integers. These as well as and many other variants have been considered. We survey some of them.
