Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Manin's conjecture for a class of singular cubic hypersurfaces   Let $n$ be a positive multiple of $4$. We establish an asymptotic formula for
the number of rational points of bounded height on singular cubic hypersurfaces
$S_n$ defined by $$ x^3=(y_1^2 + \cdots + y_n^2)z . $$ This result is new in
two aspects: first, it can be viewed as a modest start on the study of density
of rational points on those singular cubic hypersurfaces which are not covered
by the classical theorems of Davenport or Heath-Brown; second, it proves
Manin's conjecture for singular cubic hypersurfaces $S_n$ defined above.

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The categories of this paper are: supr-con
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The categories of this paper are: quant-ph
1
The categories of this paper are: cs
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The categories of this paper are: mtrl-th
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The categories of this paper are: econ
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The categories of this paper are: comp-gas
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The categories of this paper are: nlin
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The categories of this paper are: astro-ph
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The categories of this paper are: math-ph
7
The categories of this paper are: hep-th
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The categories of this paper are: gr-qc
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The categories of this paper are: atom-ph
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The categories of this paper are: q-alg
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The categories of this paper are: stat
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The categories of this paper are: adap-org
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The categories of this paper are: q-fin