Glasnik Matematicki, Vol. 41, No.2 (2006), 223-231.

TRANSCENDENCE CRITERIA FOR PAIRS OF CONTINUED FRACTIONS

Boris Adamczewski and Yann Bugeaud

CNRS, Institut Camille Jordan, Université Claude Bernard Lyon 1, Bat. Braconnier, 21 avenue Claude Bernard, 69622 Villeurbanne, Cedex, France
e-mail: Boris.Adamczewski@math.univ-lyon1.fr

Université Louis Pasteur, U. F. R. de mathématiques, 7, rue René Descartes, 67084 Strasbourg, Cedex, France
e-mail: bugeaud@math.u-strasbg.fr

Abstract.   The aim of the present note is to establish two extensions of some transcendence criteria for real numbers given by their continued fraction expansions. We adopt the following point of view: rather than giving sufficient conditions ensuring the transcendence of a given number α, we take a pair (α, α') of real numbers, and we prove that, under some condition, at least one of them is transcendental.

2000 Mathematics Subject Classification.   11J81, 11J70.

Key words and phrases.   Transcendence, continued fractions.

Full text (PDF) (free access)

DOI: 10.3336/gm.41.2.05

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