2015/12/22 by Yann Bugeaud, Bugeaud, Yann, Dong Han Kim +1 · 1 citation
Mathematics · #11A63 (primary) #68R15 (secondary) #FOS: Mathematics #Number Theory (math.NT) #math.NT #msc:11A63 #msc:68R15
paper · pdf · doi:10.48550/arxiv.1512.06935
11 pages, to appear at Annales de l'Institut Fourier
arxiv created 2016/12/12 · arxiv updated 2016/12/13
Let r and s be multiplicatively independent positive integers. We establish that the r-ary expansion and the s-ary expansion of an irrational real number, viewed as infinite words on \0, 1, … , r-1\ and \0, 1, … , s-1\, respectively, cannot have simultaneously a low block complexity. In particular, they cannot be both Sturmian words.