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arXiv · 1804.02924

Cube sums of form $3p$ and $3p^2$

Jie Shu·Xu Song·Hongbo Yin
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Abstract

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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Jie Shu, Xu Song, Hongbo Yin. 2018-04-09. Cube sums of form $3p$ and $3p^2$. https://arxiv.org/abs/1804.02924

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