Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Essential Minimum in Families of lines   We apply general methods to generate upper and lower bounds for the essential
minimum of a specific family of height functions. In particular, the results
shown in this article apply to the case of the Zhang-Zagier height.
Furthermore, we can find intervals, where the images of these heights are
dense. Our main tool to find upper bounds and intervals of density, is a
refinement of the classical Fekete-Szego theorem due to Burgos Gil, Philippon,
Rivera-Letelier and Sombra.

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The categories of this paper are: nucl-ex
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The categories of this paper are: q-fin
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The categories of this paper are: nucl-th
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The categories of this paper are: acc-phys
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The categories of this paper are: q-alg
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The categories of this paper are: dg-ga
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The categories of this paper are: eess
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The categories of this paper are: mtrl-th
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The categories of this paper are: alg-geom
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The categories of this paper are: quant-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: adap-org
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The categories of this paper are: chem-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: q-bio
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The categories of this paper are: astro-ph