Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Lower Bounds for Regulators of Number Fields in terms of their
  Discriminants   We prove inequalities that compare the regulator of a number field with its
absolute discriminant. We refine some ideas in Silverman's work in 1984 where
such general inequalities are first proven. In order to prove our main
theorems, we combine these refinements with the authors' recent results on
bounding the product of heights of relative units in a number field extension.

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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: plasm-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: quant-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: hep-lat
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The categories of this paper are: q-alg
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The categories of this paper are: astro-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: chem-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: adap-org
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The categories of this paper are: econ
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The categories of this paper are: alg-geom
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The categories of this paper are: q-fin