On Approximation constants for Liouville numbers

Abstract

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

12 pages

References in corpus (4)

• On Schmidt and Summerer parametric geometry of numbers
• On the spectrum of Diophantine approximation constants
• Diophantine approximation in small degree
• Generalizations of a result of Jarnik on simultaneous approximation

Cited by in corpus (1)

• On the spectrum of Diophantine approximation constants