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Optimal continued fractions and the moving average ergodic theorem

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Abstract

We use the moving average ergodic theorem of A. Bellow, R. Jones and J. Rosenblatt to derive various results in metric number theory primarily concerning moving averages of various sequences attached to the optimal continued fraction expansion of a real number.

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Correspondence to R. Nair.

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Communicated by István Berkes

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Haili, H.K., Nair, R. Optimal continued fractions and the moving average ergodic theorem. Period Math Hung 66, 95–103 (2013). https://doi.org/10.1007/s10998-012-7874-5

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  • DOI: https://doi.org/10.1007/s10998-012-7874-5

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