On the rational approximation to Thue--Morse rational numbers

2021/08/30 by Bugeaud, Yann, Han, Guo-Niu
#11J04 #11J70 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2108.13287

Abstract

Let b ≥ 2 and ℓ ≥ 1 be integers. We establish that there is an absolute real number K such that all the partial quotients of the rational number ∏_{h = 0}^ℓ (1 - b^-2h), of denominator b^2^ℓ+1 - 1, do not exceed exp(K (log b)² √(ℓ) 2^ℓ/2).

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