Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The degree of a $q$-holonomic sequence is a quadratic quasi-polynomial   A sequence of rational functions in a variable $q$ is $q$-holonomic if it
satisfies a linear recursion with coefficients polynomials in $q$ and $q^n$. We
prove that the degree of a $q$-holonomic sequence is eventually a quadratic
quasi-polynomial. Our proof uses differential Galois theory (adapting proofs
regarding holonomic $D$-modules to the case of $q$-holonomic $D$-modules)
combined with the Lech-Mahler-Skolem theorem from number theory. En route, we
use the Newton polygon of a linear $q$-difference equation, and introduce the
notion of regular-singular $q$-difference equation and a WKB basis of solutions
of a linear $q$-difference equation at $q=0$. We then use the
Lech-Mahler-Skolem theorem to study the vanishing of their leading term. Unlike
the case of $q=1$, there are no analytic problems regarding convergence of the
WKB solutions.Our proofs are constructive, and they are illustrated by an
explicit example.

5
The categories of this paper are: gr-qc
31
The categories of this paper are: ao-sci
9
The categories of this paper are: nlin
18
The categories of this paper are: econ
29
The categories of this paper are: funct-an
1
The categories of this paper are: cs
33
The categories of this paper are: plasm-ph
4
The categories of this paper are: cond-mat
16
The categories of this paper are: stat
25
The categories of this paper are: patt-sol
37
The categories of this paper are: supr-con
26
The categories of this paper are: bayes-an
24
The categories of this paper are: dg-ga
27
The categories of this paper are: comp-gas
8
The categories of this paper are: hep-ex
3
The categories of this paper are: physics