Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the integral of $\log x\frac{dy}{y}-\log y\frac{dx}{x}$ over the
  A-polynomial curves   In this note, we study the integral of the 1-form $\log x\frac{dy}{y}-\log
y\frac{dx}{x}$ over certain plane curves defined by A-polynomials of knots. It
is quite surprising that a Chern-Simons type invariant of 3-manifolds, which
can be geometrically computed, may be used to get the exact values of those
integrals. The arithmetic nature of these integrals is still unknown at the
moment and deserved further investigation.

18
The categories of this paper are: econ
10
The categories of this paper are: q-bio
21
The categories of this paper are: adap-org
4
The categories of this paper are: cond-mat
6
The categories of this paper are: astro-ph
25
The categories of this paper are: patt-sol
31
The categories of this paper are: ao-sci
14
The categories of this paper are: math-ph
1
The categories of this paper are: cs
35
The categories of this paper are: mtrl-th
33
The categories of this paper are: plasm-ph
3
The categories of this paper are: physics
7
The categories of this paper are: hep-th
16
The categories of this paper are: stat
30
The categories of this paper are: q-alg
34
The categories of this paper are: chem-ph