Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Modular knots, automorphic forms, and the Rademacher symbols for
  triangle groups   \'{E}.\~Ghys proved that the linking numbers of modular knots and the
"missing" trefoil $K_{2,3}$ in $S^3$ coincide with the values of a highly
ubiquitous function called the Rademacher symbol for ${\rm SL}_2\mathbb{Z}$. In
this paper, we replace ${\rm SL}_2\mathbb{Z}=\Gamma_{2,3}$ by the triangle
group $\Gamma_{p,q}$ for any coprime pair $(p,q)$ of integers with $2\leq p<q$.
We invoke the theory of harmonic Maass forms for $\Gamma_{p,q}$ to introduce
the notion of the Rademacher symbol $\psi_{p,q}$, and provide several
characterizations. Among other things, we generalize Ghys's theorem for modular
knots around any "missing" torus knot $K_{p,q}$ in $S^3$ and in a lens space.

37
The categories of this paper are: supr-con
3
The categories of this paper are: physics
21
The categories of this paper are: adap-org
9
The categories of this paper are: nlin
4
The categories of this paper are: cond-mat
25
The categories of this paper are: patt-sol
5
The categories of this paper are: gr-qc
1
The categories of this paper are: cs
12
The categories of this paper are: nucl-th
8
The categories of this paper are: hep-ex
34
The categories of this paper are: chem-ph
36
The categories of this paper are: cmp-lg
16
The categories of this paper are: stat
24
The categories of this paper are: dg-ga
0
The categories of this paper are: hep-ph
13
The categories of this paper are: quant-ph