Continued Fractions with Partial Quotients Bounded in Average

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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.
7 pages, 0 figures; minor changes, to appear in Fibonacci Quarterly

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Number Theory, Combinatorics, 11K50; 11K38

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http://salesiana.dossiersoluciones.com/handle/123456789/99895

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0310383
 http://arxiv.org/abs/math/0310383

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arXiv