Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Sidon sets for linear forms   Let $\varphi(x_1,\ldots, x_h) = c_1 x_1 + \cdots + c_h x_h $ be a linear form
with coefficients in a field $\mathbf{F}$, and let $V$ be a vector space over
$\mathbf{F}$. A nonempty subset $A$ of $V$ is a $\varphi$-Sidon set if, for all
$h$-tuples $(a_1,\ldots, a_h) \in A^h$ and $ (a'_1,\ldots, a'_h) \in A^h$, the
relation $\varphi(a_1,\ldots, a_h) = \varphi(a'_1,\ldots, a'_h)$ implies
$(a_1,\ldots, a_h) = (a'_1,\ldots, a'_h)$. There exist infinite Sidon sets for
the linear form $\varphi$ if and only if the set of coefficients of $\varphi$
has distinct subset sums. In a normed vector space with $\varphi$-Sidon sets,
every infinite sequence of vectors is asymptotic to a $\varphi$-Sidon set of
vectors. Results on $p$-adic perturbations of $\varphi$-Sidon sets of integers
and bounds on the growth of $\varphi$-Sidon sets of integers are also obtained.

20
The categories of this paper are: acc-phys
0
The categories of this paper are: hep-ph
28
The categories of this paper are: alg-geom
23
The categories of this paper are: solv-int
13
The categories of this paper are: quant-ph
10
The categories of this paper are: q-bio
36
The categories of this paper are: cmp-lg
27
The categories of this paper are: comp-gas
21
The categories of this paper are: adap-org
17
The categories of this paper are: q-fin
30
The categories of this paper are: q-alg
33
The categories of this paper are: plasm-ph
5
The categories of this paper are: gr-qc
35
The categories of this paper are: mtrl-th
31
The categories of this paper are: ao-sci
6
The categories of this paper are: astro-ph