Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On a modular form of Zaremba's conjecture   We prove that for any prime $p$ there is a divisible by $p$ number $q =
O(p^{30})$ such that for a certain positive integer $a$ coprime with $q$ the
ratio $a/q$ has bounded partial quotients. In the other direction we show that
there is an absolute constant $C>0$ such that for any prime $p$ exist divisible
by $p$ number $q = O(p^{C})$ and a number $a$, $a$ coprime with $q$ such that
all partial quotients of the ratio $a/q$ are bounded by two.

13
The categories of this paper are: quant-ph
34
The categories of this paper are: chem-ph
30
The categories of this paper are: q-alg
21
The categories of this paper are: adap-org
9
The categories of this paper are: nlin
3
The categories of this paper are: physics
14
The categories of this paper are: math-ph
18
The categories of this paper are: econ
25
The categories of this paper are: patt-sol
23
The categories of this paper are: solv-int
35
The categories of this paper are: mtrl-th
17
The categories of this paper are: q-fin
29
The categories of this paper are: funct-an
4
The categories of this paper are: cond-mat
28
The categories of this paper are: alg-geom
27
The categories of this paper are: comp-gas