Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Monic polynomials in $Z[x]$ with roots in the unit disc   This note is motivated by an old result of Kronecker on monic polynomials
with integer coefficients having all their roots in the unit disc. We call such
polynomials Kronecker polynomials for short. Let $k(n)$ denote the number of
Kronecker polynomials of degree $n$. We describe a canonical form for such
polynomials and use it to determine the sequence $k(n)$, for small values of
$n$. The first step is to show that the number of Kronecker polynomials of
degree $n$ is finite. This fact is included in the following theorem due to
Kronecker. The theorem actually gives more: the non-zero roots of such
polynomials are on the boundary of the unit disc. We use this fact later on to
show that these polynomials are essentially products of cyclotomic polynomials.

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The categories of this paper are: astro-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: quant-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: comp-gas
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The categories of this paper are: econ
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The categories of this paper are: mtrl-th
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The categories of this paper are: plasm-ph
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The categories of this paper are: hep-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: patt-sol
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The categories of this paper are: q-bio
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The categories of this paper are: chem-ph
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The categories of this paper are: nlin
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The categories of this paper are: gr-qc
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The categories of this paper are: alg-geom