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A short proof of the transcendence of Thue-Morse continued fractions. (English) Zbl 1132.11330

From the text: The Thue-Morse sequence \(t=(t_n)_{n\geq0}\) on the alphabet \(\{a,b\}\) is defined as follows: \(t_n=a\) (respectively, \(t_n=b\)) if the sum of the binary digits of \(n\) is even (respectively, odd). M. Queffélec [J. Number Theory 73, No. 2, 201–211 (1998; Zbl 0920.11045)] showed that the continued fraction is transcendental. The purpose of our note is to give a new, simpler proof of this theorem that illustrates the fruitful interplay between combinatorics on words and Diophantine approximation.

MSC:

11J70 Continued fractions and generalizations
11J81 Transcendence (general theory)

Citations:

Zbl 0920.11045
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