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arXiv · 1009.1823

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

Marc Kesseböhmer·Bernd O. Stratmann
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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.

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Marc Kesseböhmer, Bernd O. Stratmann. 2010-09-09. A dichotomy between uniform distributions of the Stern-Brocot and the Farey sequence. https://arxiv.org/abs/1009.1823

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