, Volume 105, Issue 3, pp 195-206

Limit theorems for sums of partial quotients of continued fractions

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Abstract

We prove that the partial quotientsa j of the regular continued fraction expansion cannot satisfy a strong law of large numbers for any reasonably growing norming sequence, and that thea j belong to the domain of normal attraction to a stable law with characteristic exponent 1. We also show that thea j satisfy a central limit theorem if a few of the largest ones are trimmed.

In memory of Wilfried Nöbauer