ON THE EXPANSIONS OF REAL NUMBERS IN TWO MULTIPLICATIVELY DEPENDENT BASES

초록

Let r >= 2 and s >= 2 be multiplicatively dependent integers. We establish a lower bound for the sum of the block complexities of 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}, and we show that this bound is best possible.

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