2014/07/11 by Dzmitry Badziahin, Badziahin, Dzmitry, Evgeniy Zorin +1 · 1 citation
Mathematics · #11J04 #FOS: Mathematics #Number Theory (math.NT) #math.NT #msc:11J04
paper · pdf · doi:10.48550/arxiv.1407.3182
arxiv created 2014/11/05 · arxiv updated 2014/11/06
We prove that Thue-Morse constant τTM=0.01101001...2 is not a badly approximable number. Moreover, we prove that τTM(a)=0.01101001...a is not badly approximable for every integer base a≥ 2 such that a is not divisible by 15. At the same time we provide a precise formula for convergents of the Laurent series fTM(z) = z-1∏n=1^∞ (1-z-2n), thus developing further the research initiated by Alf van der Poorten and others.