Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The number of quartic $D_4$-fields with monogenic cubic resolvent
  ordered by conductor   In this paper, we consider maximal and irreducible quartic orders which arise
from integral binary quartic forms, via the construction of Birch and Merriman,
and whose field of fractions is a quartic $D_4$-field. By a theorem of M. Wood,
such quartic orders may be regarded as quartic $D_4$-fields whose ring of
integers has a monogenic cubic resolvent. We shall give the asymptotic number
of such objects when ordered by conductor, as well as estimate the asymptotic
number of such objects when ordered by discriminant.

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The categories of this paper are: eess
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The categories of this paper are: comp-gas
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The categories of this paper are: stat
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The categories of this paper are: solv-int
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The categories of this paper are: physics
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The categories of this paper are: bayes-an
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The categories of this paper are: mtrl-th
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The categories of this paper are: chao-dyn
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The categories of this paper are: funct-an
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The categories of this paper are: hep-lat
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The categories of this paper are: quant-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: hep-ex
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The categories of this paper are: hep-ph
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The categories of this paper are: hep-th
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The categories of this paper are: astro-ph