Reprint: An arithmetic property of Taylor coefficients of rational functions (1935)
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. Reprint of the author's paper [Proc. Akad. Wet. Amsterdam 38, 50--60 (1935; Zbl 0010.39006; JFM 61.0176.02)].
scientific article; zbMATH DE number 7317815