2018
DOI: 10.1017/s0305004118000117
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On the irrationality measure of the Thue–Morse constant

Abstract: We provide a non-trivial measure of irrationality for a class of Mahler numbers defined with infinite products which cover the Thue-Morse constant. Among the other things, our results imply a generalization to [10].

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Cited by 3 publications
(5 citation statements)
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“…Therefore for s 3 − s = 0 we have that Φ(g a ) contains a primitive gap [1,3] of size 2. Note that z 3 m − s is always coprime with the polynomial z 2 + sz + s 2 .…”
Section: Lemmamentioning
confidence: 98%
See 3 more Smart Citations
“…Therefore for s 3 − s = 0 we have that Φ(g a ) contains a primitive gap [1,3] of size 2. Note that z 3 m − s is always coprime with the polynomial z 2 + sz + s 2 .…”
Section: Lemmamentioning
confidence: 98%
“…are always coprime. Therefore the all values r c,m equal zero and equations (24) imply that for the gaps [u n , v n ] generated by [1,3] we have v n+1 u n+1 = 3v n − 2 3u n and therefore lim inf…”
Section: Lemmamentioning
confidence: 99%
See 2 more Smart Citations
“…This improves the results in [14, theorem 4.1] where only an upper bound of the irrationality exponent was provided. Despite the irrationality exponents of Mahler numbers have been studied rather extensively, there is little to know about their more refined Diophantine approximation properties, we refer to the works of Badziahin and Zorin [3,5].…”
Section: Introductionmentioning
confidence: 99%