Equidistribution of digits in powers and Diophantine approximations

preprint2015arXivOpen access

Given integers $a,b>1$ with $\log_b{a}$ irrational, we investigate the connection between the conjectured asymptotic equidistribution of digits in the base- $b$ expansion of $a^n$ and the (non-)Diophantine properties of the number $θ_{a,b}=\log_b{a}$ .

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Equidistribution of digits in powers and Diophantine approximations

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