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arXiv · 2002.01223

Integer--valued functions, Hurwitz functions and related topics: a survey

Michel Waldschmidt
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Abstract

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.

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Michel Waldschmidt. 2020-02-04. Integer--valued functions, Hurwitz functions and related topics: a survey. https://arxiv.org/abs/2002.01223

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