Let $b \geq 2$ be an integer and $\alpha$ is a non-zero real number written in $b$-ary expansion. Adamczewski et al. (C. R. Acad. Sci. Paris 339 (2004) 11–14) provided a criterion for an irrational number to be a transcendental number using $b$-ary expansion. In this paper, we make some remarks on this criterion and, under the assumption of Subspace Lang Conjecture, we extend this criterion for a much wider class of irrational numbers.
Volume 131, 2021
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