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arXiv · 1409.1396

On Approximation constants for Liouville numbers

Johannes Schleischitz
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Abstract

We investigate some Diophantine approximation constants related to the simultaneous approximation of $(\zeta,\zeta^{2},\ldots,\zeta^{k})$ for Liouville numbers $\zeta$. 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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Johannes Schleischitz. 2014-09-04. On Approximation constants for Liouville numbers. https://arxiv.org/abs/1409.1396

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