Original scientific paper

https://doi.org/10.3336/gm.50.2.06

ON APPROXIMATION CONSTANTS FOR LIOUVILLE NUMBERS

Johannes Schleischitz orcid.org/0000-0002-7767-3452 ; Johannes Schleischitz Institute of Mathematics, Univ. Nat. Res. Life Sci., Gregor-Mendel-Strasse 33, Vienna, 1180, Austria

Abstract

We investigate some Diophantine approximation constants related to the simultaneous approximation of (ζ,ζ2, ...,ζk) for Liouville numbers ζ. For a certain class of Liouville numbers including the famous representative ∑n≥ 1 10-n! and numbers in the Cantor set, we explicitly determine all approximation constants simultaneously for all k≥ 1.

Keywords

Geometry of numbers; successive minima; Liouville numbers; Diophantine approximation

Hrčak ID:

150135

URI

https://hrcak.srce.hr/150135

Publication date:

29.12.2015.

Visits: 909 *