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Communication Dans Un Congrès Année : 2022

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

Résumé

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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Dates et versions

hal-04025063 , version 1 (14-03-2023)

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Michel Waldschmidt. Integer--valued functions, Hurwitz functions and related topics: a survey. 31th meeting des Journées Arithmétiques, 2019, Kağan Kurşungöz and Ayberk Zeytin, Jul 2019, Istanbul, Turkey. pp.61-82, ⟨10.1515/9783110761115-005⟩. ⟨hal-04025063⟩
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