Geodesic
On a Refinement of the Schneider–Lang theorem
Matematičeskie zametki, Tome 113 (2023) no. 6, pp. 863-875 Cet article a éte moissonné depuis la source Math-Net.Ru

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We consider some arithmetic properties of values of meromorphic functions $g_1(z)$, ..., $g_m(z)$ such that each of $g'_i(z)$ is algebraically dependent over a field $K$ of algebraic numbers, $[K:\mathbb Q]<\infty$, with the functions $g_1(z),\dots,g_m(z)$. We show that if all $\{g_i(z)\}$ are meromorphic of finite order, then either they all are rational functions, or they all are rational functions of some exponential, or they all are elliptic functions, or there exists a discrete set $U$ such that the number of points $z\notin U$ such that all $\{g_i( z)\}$ lie in $K$ is finite.
Keywords: meromorphic function, rational function. 
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V. A. Podkopaeva; A. Ya. Yanchenko. On a Refinement of the Schneider–Lang theorem. Matematičeskie zametki, Tome 113 (2023) no. 6, pp. 863-875. http://geodesic.mathdoc.fr/item/MZM_2023_113_6_a6/

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