Cube sums of form 3p and 3p2 II

Shu, Jie; Yin, Hongbo

doi:10.1007/s00208-022-02370-3

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Cube sums of form 3p and 3p² II

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Yin, Hongbo
Max Planck Institute for Mathematics, Max Planck Society;

External Resource

https://doi.org/10.1007/s00208-022-02370-3
(Publisher version)

https://doi.org/10.48550/arXiv.1909.13800
(Preprint)

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Citation

Shu, J., & Yin, H. (2023). Cube sums of form 3p and 3p² II. Mathematische Annalen, 385(3-4), 1037-1060. doi:10.1007/s00208-022-02370-3.

Cite as: https://hdl.handle.net/21.11116/0000-000A-00B8-6

Abstract

Let $p\equiv 2,5\mod 9$ be a prime. We prove that both $3p$ and $3p^2$ are
cube sums. We also establish some explicit Gross-Zagier formulae and
investigate the 3 part full BSD conjecture of the related elliptic curves.