## Reprint: Eine arithmetische Eigenschaft der Taylor-Koeffizienten rationaler Funktionen (1935)

##### Doc. Math. Extra Vol. Mahler Selecta, 437-448 (2019)
DOI: 10.25537/dm.2019.SB-437-448

### Summary

Herein, Mahler shows that, if $R(z)=\sum_{n\ge 0}G(n)z^n$ is a rational function having algebraic coefficients, infinitely many of which are zero, then there is a natural number $r$ and at most $r$ non-negative rational integers $r_1, r_2,\ldots,r_\varrho$, pairwise incongruent modulo $r$, such that only finitely many $G(n)$, with $n\equiv r_\tau\, \pmod r$ and $n\ge r_\tau$ for $\tau=1,2,\ldots,\varrho$, vanish. \par Reprint of the author's paper [Proc. Akad. Wet. Amsterdam 38, 50--60 (1935; Zbl 0010.39006; JFM 61.0176.02)].

11-03, 11J91