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Register a new userDiophantine approximation by negative continued fraction
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Authors
Hiroaki Ito
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We show that the growth rate of denominator $Q_n$ of the $n$-th convergent of negative expansion of $x$ and the rate of approximation: $$ frac{log{n}}{n}log{left|x-frac{P_n}{Q_n}right|}rightarrow -frac{pi^2}{3} quad text{in measure.} $$ for a.e. $x$. In the course of the proof, we reprove known inspiring results that arithmetic mean of digits of negative continued fraction converges to 3 in measure, although the limit inferior is 2, and the limit superior is infinite almost everywhere.
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