%0 Journal Article
%T A dichotomy between uniform distributions of the Stern-Brocot and the Farey sequence
%A Marc Kesseb£¿hmer
%A Bernd O. Stratmann
%J Uniform Distribution Theory
%D 2012
%I Mathematical Institute of the Slovak Academy of Sciences
%X We employ infinite ergodic theory to show that theeven Stern-Brocot sequence and the Farey sequence are uniformly distributed with respect to certain canonical weightings. As a corollary we derivethe precise asymptotic for the Lebesgue measure of continued fractionsum-level sets as well as connections to asymptotic behaviours of geometricallyand arithmetically restricted Poincar¨¦ series. Moreover, we give relations of our main results to elementary observations for the Stern-Brocot tree.
%K Uniform distribution
%K Stern-Brocot sequence
%K Farey sequence
%K infinite ergodic theory
%U http://www.boku.ac.at/MATH/udt/vol07/no2/02KesseboehmerStratmann15-10.pdf