Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Effective Hilbert's Irreducibility Theorem for global fields   We prove an effective form of Hilbert's irreducibility theorem for
polynomials over a global field $K$. More precisely, we give effective bounds
for the number of specializations $t\in \mathcal{O}_K$ that do not preserve the
irreducibility or the Galois group of a given irreducible polynomial $F(T,Y)\in
K[T,Y]$. The bounds are explicit in the height and degree of the polynomial
$F(T,Y)$, and are optimal in terms of the size of the parameter $t\in
\mathcal{O}_K$. Our proofs deal with the function field and number field cases
in a unified way.

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The categories of this paper are: chem-ph
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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: q-fin
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The categories of this paper are: hep-lat
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The categories of this paper are: alg-geom
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The categories of this paper are: atom-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: comp-gas
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The categories of this paper are: nlin
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The categories of this paper are: dg-ga
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The categories of this paper are: stat
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The categories of this paper are: q-bio
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The categories of this paper are: nucl-ex
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The categories of this paper are: eess