Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Weil bound and non-exceptional permutation polynomials over finite
  fields   A well-known result of von zur Gathen asserts that a non-exceptional
permutation polynomial of degree $n$ over $\mathbb{F}_{q}$ exists only if
$q<n^{4}$. With the help of the Weil bound for the number of
$\mathbb{F}_{q}$-points on an absolutely irreducible (possibly singular) affine
plane curve, Chahal and Ghorpade improved von zur Gathen's proof to replace
$n^{4}$ by a bound less than $n^{2}(n-2)^{2}$. Also based on the Weil bound, we
further refine the upper bound for $q$ with respect to $n$, by a more concise
and direct proof following Wan's arguments.

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The categories of this paper are: hep-th
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The categories of this paper are: acc-phys
28
The categories of this paper are: alg-geom
13
The categories of this paper are: quant-ph
4
The categories of this paper are: cond-mat
31
The categories of this paper are: ao-sci
1
The categories of this paper are: cs
23
The categories of this paper are: solv-int
33
The categories of this paper are: plasm-ph
37
The categories of this paper are: supr-con
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The categories of this paper are: astro-ph
36
The categories of this paper are: cmp-lg
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The categories of this paper are: hep-ex
12
The categories of this paper are: nucl-th
11
The categories of this paper are: hep-lat
16
The categories of this paper are: stat