Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Chebotarev density theorem for function fields -- incomplete
  intervals   We prove a Polya-Vinogradov type variation of the the Chebotarev density
theorem for function fields over finite fields valid for "incomplete intervals"
$I \subset \mathbb{F}_p$, provided $(p^{1/2}\log p)/|I| = o(1)$. Applications
include density results for irreducible trinomials in $\mathbb{F}_p[x]$, i.e.
the number of irreducible polynomials in the set $\{ f(x) = x^{d} + a_{1} x +
a_{0} \in \mathbb{F}_p[x] \}_{a_{0} \in I_{0}, a_{1}\in I_{1}}$ is $\sim
|I_{0}|\cdot |I_{1}|/d$ provided $|I_{0}| > p^{1/2+\epsilon}$, $|I_{1}| >
p^{\epsilon}$, or $|I_{1}| > p^{1/2+\epsilon}$, $|I_{0}| > p^{\epsilon}$, and
similarly when $x^{d}$ is replaced by any monic degree $d$ polynomial in
$\mathbb{F}_p[x]$. Under the above assumptions we can also determine the
distribution of factorization types, and find it to be consistent with the
distribution of cycle types of permutations in the symmetric group $S_{d}$.

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The categories of this paper are: supr-con
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The categories of this paper are: nucl-th
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The categories of this paper are: hep-th
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The categories of this paper are: econ
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The categories of this paper are: chem-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: alg-geom
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The categories of this paper are: plasm-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: funct-an
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The categories of this paper are: gr-qc
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The categories of this paper are: acc-phys
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The categories of this paper are: bayes-an
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The categories of this paper are: dg-ga
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The categories of this paper are: q-fin
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The categories of this paper are: hep-lat