Yann Bugeaud: Transcendental continued fractions

This is a joint work with Boris Adamczewski.

Let $ {\bf b} := (b_n)_{n \geq 1}$ be a sequence of positive integers. We give new, combinatorial conditions on the sequence $ {\bf b}$, which ensure that the real number $ [0; b_1, b_2, \ldots]$ is either quadratic, or transcendental.

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