Diophantine approximation and special Liouville numbers

This paper introduces some methods to determine the simultaneous approximation constants of a class of well approximable numbers $ζ_{1},ζ_{2},...,ζ_{k}$. The approach relies on results on the connection between the set of all $s$-adic expansions ($s\geq 2$) of $ζ_{1},ζ_{2},...,ζ_{k}$ and their associated approximation constants. As an application, explicit construction of real numbers $ζ_{1},ζ_{2},...,ζ_{k}$ with prescribed approximation properties are deduced and illustrated by Matlab plots.

No reviews yet.

No comments yet.