Geodesic
Reprint: Arithmetische Eigenschaften der Lösungen einer Klasse von Funktionalgleichungen (1929)
Documenta mathematica, Mahler Selecta (2019), pp. 191-216.

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

In this paper, Mahler introduces a method of transcendence now known as Mahler's method. He applies his method to show that the numbers \par
$ \par \par \sum_{n\ge 0} t(n)\alpha^n\quad\mbox{and}\quad\sum_{n\ge 0}\lfloor n\omega\rfloor \alpha^n \par \par $
\par are transcendental for any algebraic number $\alpha$ with $0|\alpha|1$ and any positive quadratic irrational number $\omega$, where $\{t(n)\}_{n\ge 0}$ is the Thue-Morse sequence with values in $\{-1,1\}$ and $\rfloor x\lfloor$ denotes the integer part of $x$. \par This article is the first in a series of three papers that develops Mahler's method. \par Reprint of the author's paper [Math. Ann. 101, 342--366 (1929; JFM 55.0115.01); correction 103, 532 (1930; JFM 56.0185.02)].
Classification : 11-03, 11J81
Keywords: Mahler's method 
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     author = {Mahler, Kurt},
     title = {Reprint: {Arithmetische} {Eigenschaften} der {L\"osungen} einer {Klasse} von {Funktionalgleichungen} (1929)},
     journal = {Documenta mathematica},
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     volume = {Mahler Selecta},
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Mahler, Kurt. Reprint: Arithmetische Eigenschaften der Lösungen einer Klasse von Funktionalgleichungen (1929). Documenta mathematica, Mahler Selecta (2019), pp. 191-216. http://geodesic.mathdoc.fr/item/DOCMA_2019__S1__a12/