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:

arXiv eprints
 Pub Date:
 November 2019
 DOI:
 10.48550/arXiv.1911.01821
 arXiv:
 arXiv:1911.01821
 Bibcode:
 2019arXiv191101821L
 Keywords:

 Mathematics  Number Theory
 EPrint:
 17 pages, 1 figure