Adamczewski, Boris; Bugeaud, Yann Transcendence criteria for pairs of continued fractions. (English) Zbl 1123.11023 Glas. Mat., III. Ser. 41, No. 2, 223-231 (2006). Several new transcendental criteria were made by the authors in [Acta Math. 195, No. 1, 1–20 (2005; Zbl 1195.11093), J. Reine Angew. Math. 606, 105–121 (2007; Zbl 1145.11054) and Ann. Inst. Fourier 57, No. 5, 1557–1574 (2007; Zbl 1126.11036)]. he purpose of this paper is to establish two extensions of some transcendence criteria for real numbers given by their continued fraction expansions. The authors adopt a slightly different point of view: rather than giving sufficient conditions ensuring the transcendence of a given number \(\alpha\), they take a pair \((\alpha, \alpha')\) of real numbers, and they prove that, under some condition, at least one of them is transcendental. The proofs rest on the Schmidt subspace theorem. Reviewer: Takao Komatsu (Hirosaki) Cited in 2 Documents MSC: 11J81 Transcendence (general theory) 11J70 Continued fractions and generalizations Keywords:Transcendence; continued fractions Citations:Zbl 1195.11093; Zbl 1145.11054; Zbl 1126.11036 PDFBibTeX XMLCite \textit{B. Adamczewski} and \textit{Y. Bugeaud}, Glas. Mat., III. Ser. 41, No. 2, 223--231 (2006; Zbl 1123.11023) Full Text: DOI Link