Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On Exponential Sums, Nowton identities and Dickson Polynomials over
  Finite Fields   Let $\mathbb{F}_{q}$ be a finite field, $\mathbb{F}_{q^s}$ be an extension of
$\mathbb{F}_q$, let $f(x)\in \mathbb{F}_q[x]$ be a polynomial of degree $n$
with $\gcd(n,q)=1$. We present a recursive formula for evaluating the
exponential sum $\sum_{c\in \mathbb{F}_{q^s}}\chi^{(s)}(f(x))$. Let $a$ and $b$
be two elements in $\mathbb{F}_q$ with $a\neq 0$, $u$ be a positive integer. We
obtain an estimate for the exponential sum $\sum_{c\in
\mathbb{F}^*_{q^s}}\chi^{(s)}(ac^u+bc^{-1})$, where $\chi^{(s)}$ is the lifting
of an additive character $\chi$ of $\mathbb{F}_q$. Some properties of the
sequences constructed from these exponential sums are provided also.

30
The categories of this paper are: q-alg
6
The categories of this paper are: astro-ph
31
The categories of this paper are: ao-sci
37
The categories of this paper are: supr-con
8
The categories of this paper are: hep-ex
10
The categories of this paper are: q-bio
9
The categories of this paper are: nlin
35
The categories of this paper are: mtrl-th
33
The categories of this paper are: plasm-ph
17
The categories of this paper are: q-fin
20
The categories of this paper are: acc-phys
22
The categories of this paper are: chao-dyn
13
The categories of this paper are: quant-ph
29
The categories of this paper are: funct-an
0
The categories of this paper are: hep-ph
21
The categories of this paper are: adap-org