Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Hausdorff dimension of sets with restricted, slowly growing partial
  quotients   I. J. Good (1941) showed that the set of irrational numbers in $(0,1)$ whose
partial quotients $a_n$ tend to infinity is of Hausdorff dimension $1/2$. A
number of related results impose restrictions of the type $a_n\in B$ or
$a_n\geq f(n)$, where $B$ is an infinite subset of $\mathbb N$ and $f$ is a
rapidly growing function with $n$. We show that, for an arbitrary $B$ and an
arbitrary $f$ with values in $[\min B,\infty)$ and tending to infinity, the set
of irrational numbers in $(0,1)$ such that \[ a_n\in B,\ a_n\leq f(n)\text{ for
all $n\in\mathbb N$, and }a_n\to\infty\text{ as }n\to\infty\] is of Hausdorff
dimension $\tau(B)/2,$ where $\tau(B)$ is the exponent of convergence of $B$.

37
The categories of this paper are: supr-con
11
The categories of this paper are: hep-lat
9
The categories of this paper are: nlin
17
The categories of this paper are: q-fin
15
The categories of this paper are: nucl-ex
1
The categories of this paper are: cs
10
The categories of this paper are: q-bio
30
The categories of this paper are: q-alg
23
The categories of this paper are: solv-int
25
The categories of this paper are: patt-sol
6
The categories of this paper are: astro-ph
12
The categories of this paper are: nucl-th
5
The categories of this paper are: gr-qc
22
The categories of this paper are: chao-dyn
13
The categories of this paper are: quant-ph
20
The categories of this paper are: acc-phys