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• W3034673314 abstract "Continued fraction expansions of automatic numbers have been extensively studied during the last few decades. The research interests are, on one hand, in the degree or automaticity of the partial quotients following the seminal paper of Baum and Sweet in 1976, and on the other hand, in calculating the Hankel determinants and irrationality exponents, as one can find in the works of Allouche–Peyrière–Wen–Wen, Bugeaud, and the first author. This paper is motivated by the converse problem: to study Stieltjes continued fractions whose coefficients form an automatic sequence. We consider two such continued fractions defined by the Thue–Morse and period-doubling sequences, respectively, and prove that they are congruent to algebraic series in [Formula: see text] modulo [Formula: see text]. Consequently, the sequences of the coefficients of the power series expansions of the two continued fractions modulo [Formula: see text] are [Formula: see text]-automatic." @default.
• W3034673314 created "2020-06-19" @default.
• W3034673314 creator A5051261266 @default.
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• W3034673314 date "2020-08-21" @default.
• W3034673314 modified "2023-09-25" @default.
• W3034673314 title "On the automaticity of sequences defined by the Thue–Morse and period-doubling Stieltjes continued fractions" @default.
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• W3034673314 doi "https://doi.org/10.1142/s1793042120501134" @default.
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