Boris Adamczewski & Yann Bugeaud

Transcendence criteria for pairs of continued fractions

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 $\alpha$, we take a pait $(\alpha,\alpha')$ of real numbers, and we prove that, under some condition, at least one of them is transcendental.