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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.

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  1. Department of Mathematics, University of Illinois, 1409 West Green Street, 61801, Urbana, IL, USA

    Walter Philipp

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  1. Walter Philipp
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In memory of Wilfried Nöbauer

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Philipp, W. Limit theorems for sums of partial quotients of continued fractions. Monatshefte für Mathematik 105, 195–206 (1988). https://doi.org/10.1007/BF01636928

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  • DOI: https://doi.org/10.1007/BF01636928

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