Limit theorems for sums of partial quotients of continued fractions

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