Dingding Yu

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math.NT2024

Common substring with shifts in b-ary expansions

Xin Liao, Dingding Yu

Denote by $S_{n} (x, y)$ the length of the longest common substring of $x$ and $y$ with shifts in their first $n$ digits of $b$ -ary expansions. We show that the sets of pairs $(x, y)$ ,…

math.NT2024

Metrical theory of power-2-decaying Gauss-like expansion

Zhihui Li, Xin Liao, Dingding Yu

Each $x \in (0, 1]$ can be uniquely expanded as a power-2-decaying Gauss-like expansion, in the form of \begin{equation*} x=\sum_{i=1}^{\infty}2^{-(d_1(x)+d_2(x)+\cdots+d_i(x))},\qqu…