%0 Journal Article
%T L¨¦vy constants of quadratic irrationalities
%A Christoph Baxa
%J Uniform Distribution Theory
%D 2008
%I Mathematical Institute of the Slovak Academy of Sciences
%X An irrational number $\alpha$ is said to have L¨¦vy constant $\beta(\alpha)$ if the limit $$\lim_{m \to \infty} \frac 1 m \log q_m(\alpha) =: \beta(\alpha)$$ exists where $q_m(\alpha)$ denotes the denominator of the $m$th convergent of $\alpha$. We give a new proof of the fact that the L¨¦vy constants of quadratic irrationalities are dense in the interval [\log \frac{1+ \sqrt5}2, + \infty)$.
%K Continued fraction
%K convergent
%K quadratic irrational
%U http://www.boku.ac.at/MATH/udt/vol03/no2/Baxa08-2.pdf