2015/09/01 by Badziahin, Dzmitry, Zorin, Evgeny
#11A55 #11J04 #11J70 #FOS: Mathematics #Number Theory (math.NT)
paper · doi:10.48550/arxiv.1509.00297
This paper naturally extends and generalizes our previous work "Thue-Morse constant is not badly approximable", arXiv:1407.3182 [math.NT]. Here we consider the Laurent series fd(x) = ∏n=0^∞ (1 - x-dn), d∈ℕ, d≥ 2 which generalize the generating function f2(x) of the Thue-Morse number, and study their continued fraction expansion. In particular, we show that the convergents of x-d+1fd(x) have quite a regular structure. We address as well the question whether the corresponding Mahler numbers fd(a)∈ℝ, a,d∈ℕ, a,d≥ 2, are badly approximable.