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arXiv · 1708.05266

An explicit Gross-Zagier formula related to the Sylvester Conjecture

Yueke Hu·Jie Shu·Hongbo Yin
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Abstract

Let $p\equiv 4,7\mod 9$ be a rational prime number such that $3\mod p$ is not a cubic residue. In this paper we prove the 3-part of the product of the full BSD conjectures for $E_p$ and $E_{3p^3}$ is true using an explicit Gross-Zagier formula, where $E_p: x^3+y^3=p$ and $E_{3p^2}: x^3+y^3=3p^2$ are the elliptic curves related to the Sylvester conjecture and cube sum problems.

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Yueke Hu, Jie Shu, Hongbo Yin. 2017-08-17. An explicit Gross-Zagier formula related to the Sylvester Conjecture. https://arxiv.org/abs/1708.05266

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