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math.NT2010★ 5 cited
A dichotomy between uniform distributions of the Stern-Brocot and the Farey sequence
Marc Kesseböhmer, Bernd O. Stratmann
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. A…
math.NT2005★ 70 cited
A multifractal analysis for Stern-Brocot intervals, continued fractions and Diophantine growth rates
Marc Kesseböhmer, Bernd O. Stratmann
In this paper we obtain multifractal generalizations of classical results by Lévy and Khintchin in metrical Diophantine approximations and measure theory of continued fractions. We…