Continued Fractions with Partial Quotients Bounded in Average

Details Continued Fractions with Partial Quotients Bounded in Average Continued Fractions with Partial Quotients Bounded in Average

2003-10-24

arxiv.org/abs/math/0310383v2

Mathematics

Number Theory

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

Scientific paper

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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