Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Value distribution of elementary symmetric polynomials and its
  perturbations over finite fields   In this article we establish the asymptotic behavior of generating functions
related to the exponential sum over finite fields of elementary symmetric
functions and their perturbations. This asymptotic behavior allows us to
calculate the probability generating function of the probability that the the
elementary symmetric polynomial of degree $k$ and its perturbations returns
$\beta \in \mathbb{F}_q$ where $\mathbb{F}_q$ represents the field of $q$
elements. Our study extends many of the results known for perturbations over
the binary field to any finite field. In particular, we establish when a
particular perturbation is asymptotically balanced over a prime field and
provide a construction to find such perturbations over any finite field.

14
The categories of this paper are: math-ph
13
The categories of this paper are: quant-ph
36
The categories of this paper are: cmp-lg
7
The categories of this paper are: hep-th
8
The categories of this paper are: hep-ex
3
The categories of this paper are: physics
4
The categories of this paper are: cond-mat
32
The categories of this paper are: atom-ph
34
The categories of this paper are: chem-ph
19
The categories of this paper are: eess
30
The categories of this paper are: q-alg
35
The categories of this paper are: mtrl-th
27
The categories of this paper are: comp-gas
0
The categories of this paper are: hep-ph
37
The categories of this paper are: supr-con
21
The categories of this paper are: adap-org