Glasnik matematički, Vol. 50 No. 2, 2015.
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
Publication date:
29.12.2015.
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