Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Exceptional Scattered Polynomials   Let $f$ be an $\mathbb{F}_q$-linear function over $\mathbb{F}_{q^n}$. If the
$\mathbb{F}_q$-subspace $U= \{ (x^{q^t}, f(x)) : x\in \mathbb{F}_{q^n} \}$
defines a maximum scattered linear set, then we call $f$ a scattered polynomial
of index $t$. As these polynomials appear to be very rare, it is natural to
look for some classification of them. We say a function $f$ is an exceptional
scattered polynomial of index $t$ if the subspace $U$ associated with $f$
defines a maximum scattered linear set in $\mathrm{PG}(1, q^{mn})$ for
infinitely many $m$. Our main results are the complete classifications of
exceptional scattered monic polynomials of index $0$ (for $q>5$) and of index
$1$. The strategy applied here is to convert the original question into a
special type of algebraic curves and then to use the intersection theory and
the Hasse-Weil theorem to derive contradictions.

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The categories of this paper are: eess
8
The categories of this paper are: hep-ex
18
The categories of this paper are: econ
22
The categories of this paper are: chao-dyn
12
The categories of this paper are: nucl-th
35
The categories of this paper are: mtrl-th
20
The categories of this paper are: acc-phys
16
The categories of this paper are: stat
15
The categories of this paper are: nucl-ex
6
The categories of this paper are: astro-ph
4
The categories of this paper are: cond-mat
24
The categories of this paper are: dg-ga
1
The categories of this paper are: cs
10
The categories of this paper are: q-bio
5
The categories of this paper are: gr-qc
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The categories of this paper are: alg-geom