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arXiv · 1911.01821

Multifractal analysis of the convergence exponent in continued fractions

Fang Lulu·Song Kunkun
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Abstract

Let $x \in [0,1)$ be a real number and denote its continued fraction expansion by $[a_1(x),a_2(x), a_3(x),\cdots]$. The convergence exponent of these partial quotients is defined as \[ τ(x):= \inf\left\{s \geq 0: \sum_{n \geq 1} a^{-s}_n(x)<\infty\right\}. \] In this paper, we investigate some fundamental properties and multifractal analysis of the exponent $τ(x)$.

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Fang Lulu, Song Kunkun. 2019-11-05. Multifractal analysis of the convergence exponent in continued fractions. https://arxiv.org/abs/1911.01821

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