摘要

It is a classical fact that the irrationality of a number follows from the existence of a sequence with integral and such that for all n and as . In this paper, we give an extension of this criterion in the case when the sequence possesses an additional structure; in particular, the requirement is weakened. Some applications are given, including a new proof of the irrationality of . Finally, we discuss analytical obstructions to extend the new irrationality criterion further and speculate about some mathematical constants whose irrationality is still to be established.

  • 出版日期2017-4

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