A dichotomy between uniform distributions of the Stern-Brocot and the Farey sequence

Abstract

We employ infinite ergodic theory to show that the even Stern-Brocot sequence and the Farey sequence are uniformly distributed mod 1 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.

9 pages

References in corpus (2)

• Fractal analysis for sets of non-differentiability of Minkowski's question mark function
• A note on the algebraic growth rate of Poincaré series for Kleinian groups

Cited by in corpus (1)

• A note on the algebraic growth rate of Poincaré series for Kleinian groups