Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Distributions of discriminants of cubic algebras   We study the space of binary cubic and quadratic forms over the ring of
integers $O$ of an algebraic number field $k$. By applying the theory of
prehomogeneous vector spaces founded by M. Sato and T. Shintani, we can
associate the zeta functions for these spaces. Applying these zeta functions,
we derive some density theorems on the distributions of discriminants of cubic
algebras of $O$. In the case $k$ is a quadratic field, we give a correction
term as well as the main term. These are generalizations of Shintani's
asymptotic formulae of the mean values of class numbers of binary cubic forms
over $\mathbb Z$.

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The categories of this paper are: cond-mat
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The categories of this paper are: patt-sol
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The categories of this paper are: comp-gas
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The categories of this paper are: hep-ph
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The categories of this paper are: q-fin
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The categories of this paper are: astro-ph
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The categories of this paper are: stat
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The categories of this paper are: dg-ga
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The categories of this paper are: physics
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The categories of this paper are: funct-an
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The categories of this paper are: ao-sci
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The categories of this paper are: alg-geom
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The categories of this paper are: mtrl-th
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The categories of this paper are: hep-lat
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The categories of this paper are: eess
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The categories of this paper are: hep-ex