Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Positive density of integer polynomials with some prescribed properties   In this paper, we show that various kinds of integer polynomials with
prescribed properties of their roots have positive density. For example, we
prove that almost all integer polynomials have exactly one or two roots with
maximal modulus. We also show that for any positive integer $n$ and any set of
$n$ distinct points symmetric with respect to the real line, there is a
positive density of integer polynomials of degree $n$, height at most $H$ and
Galois group $S_n$ whose roots are close to the given $n$ points.

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The categories of this paper are: hep-ex
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The categories of this paper are: astro-ph
28
The categories of this paper are: alg-geom
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The categories of this paper are: cond-mat
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The categories of this paper are: stat
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The categories of this paper are: gr-qc
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The categories of this paper are: patt-sol
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The categories of this paper are: chem-ph
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The categories of this paper are: solv-int
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The categories of this paper are: eess
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The categories of this paper are: plasm-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: comp-gas
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The categories of this paper are: atom-ph
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The categories of this paper are: q-bio
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The categories of this paper are: hep-lat