Article
Dichotomy Between Uniform Distributions of the Stern-Brocot and the Farey Sequence
Authors
and
Abstract
We employ infinite ergodic theory to show that the even Stern- Brocot sequence and the Farey sequence are uniformly distributed with respect to certain canonical weightings. As a corollary we derive the precise asymptotic for the Lebesgue measure of continued fraction sum-level sets as well as connections to asymptotic behaviours of geometrically and arithmetically restricted Poincaré series. Moreover, we give relations of our main results to elementary observations for the Stern-Brocot tree.
Keywords
Uniform distribution, Stern-Brocot sequence, Farey sequence, infinite ergodic.
Citation
Kesseböhmer, M. & Stratmann, B. O. (2012). Dichotomy between uniform distributions of the stern-brocot and the farey sequence. Uniform Distribution Theory, 7(2), 21–33.
M. Kesseböhmer and B. O. Stratmann, “Dichotomy between uniform distributions of the stern-brocot and the farey sequence,” Uniform Distribution Theory, vol. 7, no. 2, pp. 21–33, 2012.
Kesseböhmer M, Stratmann BO. Dichotomy between uniform distributions of the stern-brocot and the farey sequence. Uniform Distribution Theory. 2012;7(2):21–33.
Kesseböhmer, M. and Stratmann, B. O. (2012), ‘Dichotomy between uniform distributions of the stern-brocot and the farey sequence’, Uniform Distribution Theory, 7(2), pp. 21–33.
Kesseböhmer, Marc, and Bernd O. Stratmann. “Dichotomy Between Uniform Distributions of the Stern-brocot and the Farey Sequence.” Uniform Distribution Theory, vol. 7, no. 2, 2012, pp. 21–33.
Kesseböhmer, Marc, and Bernd O. Stratmann. “Dichotomy Between Uniform Distributions of the Stern-brocot and the Farey Sequence.” Uniform Distribution Theory 7, no. 2 (2012): 21–33.
Export citation
Published by: Engineering Journals
