Geodesic
On a Class of Integer-Valued Functions
Matematičeskie zametki, Tome 107 (2020) no. 5, pp. 760-773

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The paper deals with the class of entire functions that increase not faster than $\exp\{\gamma|z|^{6/5}(\ln|z|)^{-1}\}$ and that, together with their first derivatives, take values from a fixed field of algebraic numbers at the points of a two-dimensional lattice of general form (in this case, the values increase not too fast). It is shown that any such functions is either a polynomial or can be represented in the form $e^{-m\alpha z}P(e^{\alpha z})$, where $m$ is a nonnegative integer, $P$ is a polynomial, and $\alpha$ is an algebraic number.
Keywords: entire function, algebraic values. 
@article{MZM_2020_107_5_a7,
     author = {A. Y. Yanchenko and V. A. Podkopaeva},
     title = {On a {Class} of {Integer-Valued} {Functions}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {760--773},
     publisher = {mathdoc},
     volume = {107},
     number = {5},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2020_107_5_a7/}
}
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A. Y. Yanchenko; V. A. Podkopaeva. On a Class of Integer-Valued Functions. Matematičeskie zametki, Tome 107 (2020) no. 5, pp. 760-773. http://geodesic.mathdoc.fr/item/MZM_2020_107_5_a7/