ON THE EXPANSIONS OF REAL NUMBERS IN TWO INTEGER BASES

초록

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.

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