Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Cube sums of form $3p$ and $3p^2$   Let $p\equiv 2,5\mod 9$ be an odd prime. In this paper, we prove that at
least one of $3p$ and $3p^2$ is a cube sum by constructing certain nontrivial
Heegner points. We also establish the explicit Gross-Zagier formulae for these
Heegner points and give variants of the Birch and Swinnerton-Dyer conjecture of
the related elliptic curves.

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The categories of this paper are: q-alg
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The categories of this paper are: chem-ph
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The categories of this paper are: solv-int
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The categories of this paper are: patt-sol
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The categories of this paper are: eess
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The categories of this paper are: astro-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: q-fin
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The categories of this paper are: quant-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: supr-con
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The categories of this paper are: econ
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The categories of this paper are: dg-ga
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The categories of this paper are: nucl-ex
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The categories of this paper are: math-ph
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The categories of this paper are: cond-mat