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ON THE EXPANSIONS OF REAL NUMBERS IN TWO MULTIPLICATIVELY DEPENDENT BASES
- Part of
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- Journal:
- Bulletin of the Australian Mathematical Society / Volume 95 / Issue 3 / June 2017
- Published online by Cambridge University Press:
- 01 December 2016, pp. 373-383
- Print publication:
- June 2017
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- Article
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Let
$r\geq 2$ and 
$s\geq 2$ 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 
$\{0,1,\ldots ,r-1\}$ and 
$\{0,1,\ldots ,s-1\}$, and we show that this bound is best possible.
