On Approximation constants for Liouville numbers

We investigate some Diophantine approximation constants related to the simultaneous approximation of $(ζ,ζ^{2},\ldots,ζ^{k})$ for Liouville numbers $ζ$. For a certain class of Liouville numbers including the famous representative $\sum_{n\geq 1} 10^{-n!}$ and numbers in the Cantor set, we explicitly determine all approximation constants simultaneously for all $k\geq 1$.

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