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    Fractional dimension of some exceptional sets in continued fractions

    Fractional dimension of some exceptional sets in continued fractions by Hussain, Mumtaz, Smith, Rebecca, Zhang, Zhenliang

    Published 2025-03-01

    In this paper, we calculate the Hausdorff dimension of some exceptional sets that emerge from specific constraints imposed on the partial quotients of continued fractions. In particular, we calculate the Hausdorff dimension of the sets \[ \Lambda _1=\Biggl \lbrace x\in (0,1): a_{n+1}(x)\ge \sum _{i=...

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