2020/02/04 by Michel Waldschmidt, Waldschmidt, Michel
Mathematics · #Meromorphic and Entire Functions
paper · doi:10.48550/arxiv.2002.01223
An integer--valued function is an entire function which maps the nonnegative integers \mathbb N to the integers. An example is 2z. A Hurwitz function is an entire function having all derivatives taking integer values at 0. An example is \mathrm ez. 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.