Glasnik Matematicki, Vol. 50, No. 2 (2015), 349-361.

ON APPROXIMATION CONSTANTS FOR LIOUVILLE NUMBERS

Johannes Schleischitz

Institute of Mathematics, Univ. Nat. Res. Life Sci., Gregor-Mendel-Strasse 33, Vienna, 1180, Austria
e-mail: johannes.schleischitz@boku.ac.at

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.

2010 Mathematics Subject Classification.   11J13, 11J25, 11J82.

Key words and phrases.   Geometry of numbers, successive minima, Liouville numbers, Diophantine approximation.

Full text (PDF) (free access)

DOI: 10.3336/gm.50.2.06

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