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Continued Fractions with Partial Quotients Bounded in Average

Joshua N. Cooper
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Abstract

We ask, for which $n$ does there exists a $k$, $1 \leq k < n$ and $(k,n)=1$, so that $k/n$ has a continued fraction whose partial quotients are bounded in average by a constant $B$? This question is intimately connected with several other well-known problems, and we provide a lower bound in the case of B=2.

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Joshua N. Cooper. 2006-02-28. Continued Fractions with Partial Quotients Bounded in Average. https://arxiv.org/abs/math/0310383

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