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arXiv · 1801.03120

Limiting curves for the dyadic odometer and the generalized Trollope-Delange formula

Aleksei Minabutdinov
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Abstract

We study limiting curves resulting from deviations in partial sums in the ergodic theorem for the dyadic odometer and non-cylindric functions. In particular, we generalize the Trollope-Delange formula for the case of the weighted sum-of-binary-digits function and show that the Takagi-Landsberg curve arises.

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Aleksei Minabutdinov. 2018-01-09. Limiting curves for the dyadic odometer and the generalized Trollope-Delange formula. https://arxiv.org/abs/1801.03120

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