A short proof of the transcendence of Thue-Morse continued fractions

American Mathematical Monthly

Volumn 114, Issue 6, 2007, Pages 536-540

  Adamczewski, Boris ^a   Bugeaud, Yann ^b  

^a UNIVERSITÉ LYON 1   (France)

^b UNIVERSITÉ DE STRASBOURG   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 34248511808     PISSN: 00029890     EISSN: None     Source Type: Journal    
DOI: 10.1080/00029890.2007.11920443     Document Type: Article

References (14)

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2. F. M. Dekking, Transcendance du nombre de Thue-Morse, C. R. Acad. Sci. Paris 285 (1977) 157-160.
3. J. S. Frame, Continued fractions and matrices, this MONTHLY 56 (1949) 98-103.
4. A. Ya. Khintchin, Continued Fractions, 2nd ed., Gosudarstv. Izdat. Tehn.-Theor. Lit. Moscow-Leningrad, 1949 (Russian); English translation, University of Chicago Press, Chicago-London, 1964.
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9. _, Irrational numbers with automaton-generated continued fraction expansion, in Dynamical systems (Lummy-Marseille, 1998), World Scientific, River Edge, NJ, 2000, pp. 190-198.
10. W. M. Schmidt, On simultaneous approximations of two algebraic numbers by rationals, Acta Math. 119 (1967) 27-50.
11. J. O. Shallit, Real numbers with bounded partial quotients, Enseign. Math. 38 (1992) 151-187.
12. A. Thue, Über die gegenseitige Lage gleicher Teile gewisser Zeichenreihen, Norske vid. Selsk. Skr. Mat. Nat. Kl. 1 (1912) 1-67;
13. reprinted in Selected Mathematical Papers of Axel Thue, T. Nageil, ed., Universitetsforlaget, Oslo, 1977, pp. 413-478.
14. M. Waldschmidt, Un demi-siècle de transcendance, in Development of Mathematics 1950-2000, Birkhäuser, Basel, 2000, pp. 1121-1186.