On the Expansions of Real Numbers in Two Integer Bases
نویسندگان
چکیده
Let r ≥ 2 and s ≥ 2 be distinct integers. We establish that, if r and s are multiplicatively independent, then 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. We also discuss the case where r and s are multiplicatively dependent.
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تاریخ انتشار 2015