Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Salem numbers and Pisot numbers via interlacing   We present a general construction of Salem numbers via rational functions
whose zeros and poles mostly lie on the unit circle and satisfy an interlacing
condition. This extends and unifies earlier work. We then consider the
"obvious" limit points of the set of Salem numbers produced by our theorems,
and show that these are all Pisot numbers, in support of a conjecture of Boyd.
We then show that all Pisot numbers arise in this way. Combining this with a
theorem of Boyd, we show that all Salem numbers are produced via an interlacing
construction.

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The categories of this paper are: adap-org
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The categories of this paper are: mtrl-th
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The categories of this paper are: acc-phys
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The categories of this paper are: eess
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The categories of this paper are: solv-int
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The categories of this paper are: chem-ph
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The categories of this paper are: q-alg
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The categories of this paper are: nlin
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The categories of this paper are: hep-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: econ
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The categories of this paper are: q-fin
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The categories of this paper are: atom-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: nucl-th
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The categories of this paper are: quant-ph