Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Explicit Hilbert's Irreducibility Theorem in Function Fields   We prove a quantitative version of Hilbert's irreducibility theorem for
function fields: If $f(T_1,\ldots, T_n,X)$ is an irreducible polynomial over
the field of rational functions over a finite field $\mathbb{F}_q$ of
characteristic $p$, then the proportion of $n$-tuples $(t_1,\ldots, t_n)$ of
monic polynomials of degree $d$ for which $f(t_1,\ldots, t_n,X)$ is reducible
out of all $n$-tuples of degree $d$ monic polynomials is $O(dq^{-d/2})$.

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The categories of this paper are: math-ph
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The categories of this paper are: solv-int
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The categories of this paper are: nucl-ex
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The categories of this paper are: cs
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The categories of this paper are: atom-ph
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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: plasm-ph
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The categories of this paper are: supr-con
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The categories of this paper are: stat
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The categories of this paper are: comp-gas
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The categories of this paper are: cond-mat
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The categories of this paper are: bayes-an
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The categories of this paper are: astro-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: cmp-lg