Multifractal analysis of the convergence exponent in continued fractions
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 \[ \tau(x):= \inf\left\{s \geq 0: \sum_{n \geq 1} a^{-s}_n(x)<\infty\right\}. \] In this paper, we investigate some fundamental properties and multifractal analysis of the exponent $\tau(x)$.
- Publication:
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arXiv e-prints
- Pub Date:
- November 2019
- DOI:
- 10.48550/arXiv.1911.01821
- arXiv:
- arXiv:1911.01821
- Bibcode:
- 2019arXiv191101821L
- Keywords:
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- Mathematics - Number Theory
- E-Print:
- 17 pages, 1 figure