Diophantine approximation and special Liouville numbers

Abstract

This paper introduces some methods to determine the simultaneous approximation constants of a class of well approximable numbers ${\zeta }_1,{\zeta }_2,...,{\zeta }_k$. The approach relies on results on the connection between the set of all $s$-adic expansions ($s\ge 2$) of ${\zeta }_1,{\zeta }_2,...,{\zeta }_k$ and their associated approximation constants. As an application, explicit construction of real numbers ${\zeta }_1,{\zeta }_2,...,{\zeta }_k$ with prescribed approximation properties are deduced and illustrated by Matlab plots.

30 pages, 3 figures

References in corpus (1)

• Proof of W.M.Schmidt's conjecture concerning successive minima of a lattice

Cited by in corpus (1)

• A variational principle in the parametric geometry of numbers, with applications to metric Diophantine approximation