Reprint: Remarks on a paper by W. Schwarz (1969)
type: Item
instance of: scholarly article
title: Reprint: Remarks on a paper by W. Schwarz (1969)
zbMATH Open document ID: 1457.11004
published in: Documenta Mathematica
publication date: 2021-03-05T00:00:00Z
review text: Summary: Mahler reports on old work of his on the transcendency of functions that satisfy functional equations such as \[ F(z^2)=\frac{(1-z)F(z)-z}{1-z}. \] He suggests a number of directions in which this work might possibly be extended. This paper re-invigorated the area of transcendence theory that is now known as Mahler's method. Reprint of the author's paper [J. Number Theory 1, 512--521 (1969; Zbl 0184.07602)]. The paper by \textit{W. Schwarz} mentioned in the title appeared in [Math. Scand. 20, 269--274 (1967; Zbl 0164.05701)]. Mahler observed that Schwarz did not cite his papers in [Math. Ann. 101, 342--346 (1929; JFM 55.0115.01); 103, 573--587 (1930; JFM 56.0185.03); Math. Z. 32, 545--585 (1930; JFM 56.0186.01)] in which the problem of the transcendency of functions like \(G_k(z)\) was solved for all algebraic values of \(z\), and very general theorems were proved.
Mathematics Subject Classification ID: 11-03
Mathematics Subject Classification ID: 11J85
zbMATH DE Number: 7317831
zbMATH Keywords: Mahler's method
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.4171/dms/8/40
OpenAlex ID: W4361793052
DOI: 10.4171/DMS/8/40
author: Kurt Mahler
Recommended article: Q3724413
Recommended article: Remarks on a Paper by R. M. Hirschorn
Recommended article: Q5850597
Recommended article: A note on a paper by W. J. Ricker and H. H. Schaefer
Recommended article: Remarks on a paper by Maharaj and Wulftange
Recommended article: A remark on a result of Schwaiger
Recommended article: Q5187353
Recommended article: Q3361397
Recommended article: Some remarks on a paper by L. Carlitz
Recommended article: A note on some results of Schwick
description: scientific article; zbMATH DE number 7317831