Mahler, Kurt

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


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)].

Mathematics Subject Classification

11-03, 11J91