RÉSUMÉ

We give new irrationality criteria for the Cantor series $\sum_{n\geq 1} b_n/(a_1 \cdots a_n)$ and for the series $\sum_{n\geq 1} b_n/a_n$, where $a_1, a_2, ...$ and $b_1, b_2, ...$ are integers such that $a_n>0$ and the series converge. We show by examples that such results are impossible without growth restrictions.

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