Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On upper and lower fast Knintchine spectra of continued fractions   Let $\psi:\mathbb{N}\to \mathbb{R}^+$ be a function satisfying $\phi(n)/n\to
\infty$ as $n \to \infty$. We investigate from a multifractal analysis point of
view the growth rate of the sums $\sum^n_{k=1}\log a_k(x)$ relative to
$\psi(n)$, where $[a_1(x),a_2(x), a_3(x)\cdots]$ denotes the continued fraction
expansion of $x\in (0,1)$. The upper (resp. lower) fast Khintchine spectrum is
defined by the Hausdorff dimension of the set of all points $x$ for which the
upper (resp. lower) limit of $\frac{1}{\psi(n)}\sum^n_{k=1}\log a_k(x)$ is $1$.
The precise formulas of these two spectra are completely determined, which
strengthens a result of Liao and Rams (2016).

10
The categories of this paper are: q-bio
4
The categories of this paper are: cond-mat
3
The categories of this paper are: physics
35
The categories of this paper are: mtrl-th
15
The categories of this paper are: nucl-ex
7
The categories of this paper are: hep-th
28
The categories of this paper are: alg-geom
8
The categories of this paper are: hep-ex
23
The categories of this paper are: solv-int
6
The categories of this paper are: astro-ph
11
The categories of this paper are: hep-lat
18
The categories of this paper are: econ
25
The categories of this paper are: patt-sol
30
The categories of this paper are: q-alg
36
The categories of this paper are: cmp-lg
21
The categories of this paper are: adap-org