Geodesic
Reprint: Remarks on a paper by W. Schwarz (1969)
Documenta mathematica, Mahler Selecta (2019), pp. 649-659.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Mahler reports on old work of his on the transcendency of functions that satisfy functional equations such as
$ \par \par F(z^2)=\frac{(1-z)F(z)-z}{1-z}. \par \par $
\par 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. \par Reprint of the author's paper [J. Number Theory 1, 512--521 (1969; Zbl 0184.07602)]. \par 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.
Classification : 11-03, 11J85
Keywords: Mahler's method 
@article{DOCMA_2019__S1__a39,
     author = {Mahler, Kurt},
     title = {Reprint: {Remarks} on a paper by {W.} {Schwarz} (1969)},
     journal = {Documenta mathematica},
     pages = {649--659},
     publisher = {mathdoc},
     volume = {Mahler Selecta},
     year = {2019},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DOCMA_2019__S1__a39/}
}
TY  - JOUR
AU  - Mahler, Kurt
TI  - Reprint: Remarks on a paper by W. Schwarz (1969)
JO  - Documenta mathematica
PY  - 2019
SP  - 649
EP  - 659
VL  - Mahler Selecta
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DOCMA_2019__S1__a39/
LA  - en
ID  - DOCMA_2019__S1__a39
ER  - 
%0 Journal Article
%A Mahler, Kurt
%T Reprint: Remarks on a paper by W. Schwarz (1969)
%J Documenta mathematica
%D 2019
%P 649-659
%V Mahler Selecta
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DOCMA_2019__S1__a39/
%G en
%F DOCMA_2019__S1__a39
Mahler, Kurt. Reprint: Remarks on a paper by W. Schwarz (1969). Documenta mathematica, Mahler Selecta (2019), pp. 649-659. http://geodesic.mathdoc.fr/item/DOCMA_2019__S1__a39/