Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Reverse asymptotic estimates for roots of the cuboid characteristic
  equation in the case of the second cuboid conjecture   A perfect cuboid is a rectangular parallelepiped whose edges, whose face
diagonals, and whose space diagonal are of integer lengths. The second cuboid
conjecture specifies a subclass of perfect cuboids described by one Diophantine
equation of tenth degree and claims their non-existence within this subclass.
This Diophantine equation has two parameters. Previously asymptotic expansions
and estimates for roots of this equation were obtained in the case where the
first parameter is fixed and the other tends to infinity. In the present paper
reverse asymptotic expansions and estimates are derived in the case where the
second parameter is fixed and the first one tends to infinity. Their
application to the perfect cuboid problem is discussed.

16
The categories of this paper are: stat
34
The categories of this paper are: chem-ph
24
The categories of this paper are: dg-ga
3
The categories of this paper are: physics
17
The categories of this paper are: q-fin
6
The categories of this paper are: astro-ph
15
The categories of this paper are: nucl-ex
19
The categories of this paper are: eess
31
The categories of this paper are: ao-sci
37
The categories of this paper are: supr-con
35
The categories of this paper are: mtrl-th
29
The categories of this paper are: funct-an
18
The categories of this paper are: econ
28
The categories of this paper are: alg-geom
5
The categories of this paper are: gr-qc
13
The categories of this paper are: quant-ph