Reprint: Arithmetic properties of solutions of a class of functional equations (1929)
Kurt Mahler
Abstract
In this paper, Mahler introduces a method of transcendence now known as Mahler's method. He applies his method to show that the numbers
are transcendental for any algebraic number with and any positive quadratic irrational number , where {t(n)\}_{n\ge 0} is the Thue-Morse sequence with values in {-1,1\} and denotes the integer part of .
This article is the first in a series of three papers that develops Mahler's method.
Reprint of the author's paper [Math. Ann. 101, 342--366 (1929; JFM 55.0115.01); correction 103, 532 (1930; JFM 56.0185.02)].