Haibo Chen

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math.NT2018

Hausdorff dimensions of level sets related to moving digit means

Haibo Chen

In this paper, we will introduce and study the lower moving digit mean $M (x)$ and the upper moving digit mean $M (x)$ of $x \in [0, 1]$ in $p$ -adic expansion, wh…

math.NT2018

Hausdorff dimensions of sets related to Erdös-Rényi averages in beta expansions

Haibo Chen

Let $β > 1$ , $I$ be the unite interval $[0, 1)$ and $ϕ$ be an integer function defined on $N ∖ {0}$ satisfying $1 \leq ϕ (n) \leq n$ . Denote by $A_{ϕ} (x, β)$ the Erdös-Rényi…