Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Linear forms and complementing sets of integers   Let $\varphi(x_1,\ldots,x_h,y) = u_1x_1 + \cdots + u_hx_h+vy$ be a linear
form with nonzero integer coefficients $u_1,\ldots, u_h, v.$ Let $\mathcal{A} =
(A_1,\ldots, A_h)$ be an $h$-tuple of finite sets of integers and let $B$ be an
infinite set of integers. Define the representation function associated to the
form $\varphi$ and the sets \mca\ and $B$ as follows: $$
R^{(\varphi)}_{\mathcal{A},B}(n) = \text{card}\left( \left\{ (a_1,\ldots,
a_h,b) \in A_1 \times \cdots \times A_h \times B: \varphi(a_1, \ldots , a_h,b )
= n \right\} \right).$$ If this representation function is constant, then the
set $B$ is periodic and the period of $B$ will be bounded in terms of the
diameter of the finite set $\{ \varphi(a_1,\ldots,a_h,0): (a_1,\ldots, a_h) \in
A_1 \times \cdots \times A_h\}.$

17
The categories of this paper are: q-fin
24
The categories of this paper are: dg-ga
14
The categories of this paper are: math-ph
21
The categories of this paper are: adap-org
9
The categories of this paper are: nlin
18
The categories of this paper are: econ
12
The categories of this paper are: nucl-th
28
The categories of this paper are: alg-geom
1
The categories of this paper are: cs
31
The categories of this paper are: ao-sci
29
The categories of this paper are: funct-an
23
The categories of this paper are: solv-int
32
The categories of this paper are: atom-ph
25
The categories of this paper are: patt-sol
15
The categories of this paper are: nucl-ex
0
The categories of this paper are: hep-ph