Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The number of 2x2 integer matrices having a prescribed integer
  eigenvalue   Random matrices arise in many mathematical contexts, and it is natural to ask
about the properties that such matrices satisfy. If we choose a matrix with
integer entries at random, for example, what is the probability that it will
have a particular integer as an eigenvalue, or an integer eigenvalue at all? If
we choose a matrix with real entries at random, what is the probability that it
will have a real eigenvalue in a particular interval? The purpose of this paper
is to resolve these questions, once they are made suitably precise, in the
setting of 2x2 matrices.

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The categories of this paper are: physics
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The categories of this paper are: cmp-lg
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The categories of this paper are: hep-lat
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The categories of this paper are: astro-ph
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The categories of this paper are: patt-sol
29
The categories of this paper are: funct-an
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The categories of this paper are: cs
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The categories of this paper are: hep-ex
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The categories of this paper are: q-alg
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The categories of this paper are: atom-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: eess
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The categories of this paper are: q-bio
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The categories of this paper are: quant-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: comp-gas